Hydrogen bond
A hydrogen bond is a electrostatic force of attraction between a hydrogen atom, covalently bound to a more electronegative atom or group the second-row elements nitrogen, oxygen, or fluorine —the hydrogen bond donor —and another electronegative atom bearing a lone pair of electrons—the hydrogen bond acceptor. Such an interacting system is denoted Dn–H···Ac, where the solid line denotes a covalent bond, the dotted line indicates the hydrogen bond. There is general agreement that there is a minor covalent component to hydrogen bonding for moderate to strong hydrogen bonds, although the importance of covalency in hydrogen bonding is debated. At the opposite end of the scale, there is no clear boundary between a weak hydrogen bond and a van der Waals interaction. Weaker hydrogen bonds are known for hydrogen atoms bound to elements such as chlorine; the hydrogen bond is responsible for many of the anomalous physical and chemical properties of compounds of N, O, F. Hydrogen bonds can be intramolecular.
Depending on the nature of the donor and acceptor atoms which constitute the bond, their geometry, environment, the energy of a hydrogen bond can vary between 1 and 40 kcal/mol. This makes them somewhat stronger than a van der Waals interaction, weaker than covalent or ionic bonds; this type of bond can occur in inorganic molecules such as water and in organic molecules like DNA and proteins. Intermolecular hydrogen bonding is responsible for the high boiling point of water compared to the other group 16 hydrides that have much weaker hydrogen bonds. Intramolecular hydrogen bonding is responsible for the secondary and tertiary structures of proteins and nucleic acids, it plays an important role in the structure of polymers, both synthetic and natural. It was recognized that there are many examples of weaker hydrogen bonding involving donor Dn other than N, O, or F and/or acceptor Ac with close to or the same electronegativity as hydrogen. Though they are quite weak, they are ubiquitous and are recognized as important control elements in receptor-ligand interactions in medicinal chemistry or intra-/intermolecular interactions in materials sciences.
Thus, there is a trend of gradual broadening for the definition of hydrogen bonding. In 2011, an IUPAC Task Group recommended a modern evidence-based definition of hydrogen bonding, published in the IUPAC journal Pure and Applied Chemistry; this definition specifies: The hydrogen bond is an attractive interaction between a hydrogen atom from a molecule or a molecular fragment X–H in which X is more electronegative than H, an atom or a group of atoms in the same or a different molecule, in which there is evidence of bond formation. Most introductory textbooks still restrict the definition of hydrogen bond to the "classical" type of hydrogen bond characterized in the opening paragraph. A hydrogen atom attached to a electronegative atom is the hydrogen bond donor. C-H bonds only participate in hydrogen bonding when the carbon atom is bound to electronegative substituents, as is the case in chloroform, CHCl3. In a hydrogen bond, the electronegative atom not covalently attached to the hydrogen is named proton acceptor, whereas the one covalently bound to the hydrogen is named the proton donor.
In the donor molecule, the H center is protic. The donor is a Lewis base. Hydrogen bonds are represented as H · · · Y system. Liquids that display hydrogen bonding are called associated liquids; the hydrogen bond is described as an electrostatic dipole-dipole interaction. However, it has some features of covalent bonding: it is directional and strong, produces interatomic distances shorter than the sum of the van der Waals radii, involves a limited number of interaction partners, which can be interpreted as a type of valence; these covalent features are more substantial when acceptors bind hydrogens from more electronegative donors. Hydrogen bonds can vary in strength from weak to strong. Typical enthalpies in vapor include: F−H···:F, illustrated uniquely by HF2−, bifluoride O−H···:N, illustrated water-ammonia O−H···:O, illustrated water-water, alcohol-alcohol N−H···:N, illustrated by ammonia-ammonia N−H···:O, illustrated water-amide HO−H···:OH+3 The strength of intermolecular hydrogen bonds is most evaluated by measurements of equilibria between molecules containing donor and/or acceptor units, most in solution.
The strength of intramolecular hydrogen bonds can be studied with equilibria between conformers with and without hydrogen bonds. The most important method for the identification of hydrogen bonds in complicated molecules is crystallography, sometimes NMR-spectroscopy. Structural details, in particular distances between donor and acceptor which are smaller than the sum of the van der Waals radii can be taken as indication of the hydrogen bond strength. One scheme gives the following somewhat arbitrary classification: those that are 15 to 40 kcal/mol, 5 to 15 kcal/mol, >0 to 5 kcal/mol are considered strong, moder
Entropy
In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is related to the number Ω of microscopic configurations that are consistent with the macroscopic quantities that characterize the system. Under the assumption that each microstate is probable, the entropy S is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant kB. Formally, S = k B ln Ω. Macroscopic systems have a large number Ω of possible microscopic configurations. For example, the entropy of an ideal gas is proportional to the number of gas molecules N. Twenty liters of gas at room temperature and atmospheric pressure has N ≈ 6×1023. At equilibrium, each of the Ω ≈ eN configurations can be regarded as random and likely; the second law of thermodynamics states. Such systems spontaneously evolve towards the state with maximum entropy. Non-isolated systems may lose entropy, provided their environment's entropy increases by at least that amount so that the total entropy increases.
Entropy is a function of the state of the system, so the change in entropy of a system is determined by its initial and final states. In the idealization that a process is reversible, the entropy does not change, while irreversible processes always increase the total entropy; because it is determined by the number of random microstates, entropy is related to the amount of additional information needed to specify the exact physical state of a system, given its macroscopic specification. For this reason, it is said that entropy is an expression of the disorder, or randomness of a system, or of the lack of information about it; the concept of entropy plays a central role in information theory. Boltzmann's constant, therefore entropy, have dimensions of energy divided by temperature, which has a unit of joules per kelvin in the International System of Units; the entropy of a substance is given as an intensive property—either entropy per unit mass or entropy per unit amount of substance. The French mathematician Lazare Carnot proposed in his 1803 paper Fundamental Principles of Equilibrium and Movement that in any machine the accelerations and shocks of the moving parts represent losses of moment of activity.
In other words, in any natural process there exists an inherent tendency towards the dissipation of useful energy. Building on this work, in 1824 Lazare's son Sadi Carnot published Reflections on the Motive Power of Fire which posited that in all heat-engines, whenever "caloric" falls through a temperature difference, work or motive power can be produced from the actions of its fall from a hot to cold body, he made the analogy with that of. This was an early insight into the second law of thermodynamics. Carnot based his views of heat on the early 18th century "Newtonian hypothesis" that both heat and light were types of indestructible forms of matter, which are attracted and repelled by other matter, on the contemporary views of Count Rumford who showed that heat could be created by friction as when cannon bores are machined. Carnot reasoned that if the body of the working substance, such as a body of steam, is returned to its original state at the end of a complete engine cycle, that "no change occurs in the condition of the working body".
The first law of thermodynamics, deduced from the heat-friction experiments of James Joule in 1843, expresses the concept of energy, its conservation in all processes. In the 1850s and 1860s, German physicist Rudolf Clausius objected to the supposition that no change occurs in the working body, gave this "change" a mathematical interpretation by questioning the nature of the inherent loss of usable heat when work is done, e.g. heat produced by friction. Clausius described entropy as the transformation-content, i.e. dissipative energy use, of a thermodynamic system or working body of chemical species during a change of state. This was in contrast to earlier views, based on the theories of Isaac Newton, that heat was an indestructible particle that had mass. Scientists such as Ludwig Boltzmann, Josiah Willard Gibbs, James Clerk Maxwell gave entropy a statistical basis. In 1877 Boltzmann visualized a probabilistic way to measure the entropy of an ensemble of ideal gas particles, in which he defined entropy to be proportional to the natural logarithm of the number of microstates such a gas could occupy.
Henceforth, the essential problem in statistical thermodynamics, i.e. according to Erwin Schrödinger, has been to determine the distribution of a given amount of energy E over N identical systems. Carathéodory linked entropy with a mathematical definition of irreversibility, in terms of trajectories and integrability. There are two related definitions of entropy: the thermodynamic definition and the statistical mechanics definition; the classical thermodynamics definition developed first. In the classical thermodynamics viewpoint, the system is composed of large numbers of constituents and the state of the system is described by the average thermodynamic properties of those constituents.
DNA
Deoxyribonucleic acid is a molecule composed of two chains that coil around each other to form a double helix carrying the genetic instructions used in the growth, development and reproduction of all known organisms and many viruses. DNA and ribonucleic acid are nucleic acids; the two DNA strands are known as polynucleotides as they are composed of simpler monomeric units called nucleotides. Each nucleotide is composed of one of four nitrogen-containing nucleobases, a sugar called deoxyribose, a phosphate group; the nucleotides are joined to one another in a chain by covalent bonds between the sugar of one nucleotide and the phosphate of the next, resulting in an alternating sugar-phosphate backbone. The nitrogenous bases of the two separate polynucleotide strands are bound together, according to base pairing rules, with hydrogen bonds to make double-stranded DNA; the complementary nitrogenous bases are divided into two groups and purines. In DNA, the pyrimidines are cytosine. Both strands of double-stranded DNA store the same biological information.
This information is replicated as and when the two strands separate. A large part of DNA is non-coding, meaning that these sections do not serve as patterns for protein sequences; the two strands of DNA are thus antiparallel. Attached to each sugar is one of four types of nucleobases, it is the sequence of these four nucleobases along the backbone. RNA strands are created using DNA strands as a template in a process called transcription. Under the genetic code, these RNA strands specify the sequence of amino acids within proteins in a process called translation. Within eukaryotic cells, DNA is organized into long structures called chromosomes. Before typical cell division, these chromosomes are duplicated in the process of DNA replication, providing a complete set of chromosomes for each daughter cell. Eukaryotic organisms store most of their DNA inside the cell nucleus as nuclear DNA, some in the mitochondria as mitochondrial DNA, or in chloroplasts as chloroplast DNA. In contrast, prokaryotes store their DNA only in circular chromosomes.
Within eukaryotic chromosomes, chromatin proteins, such as histones and organize DNA. These compacting structures guide the interactions between DNA and other proteins, helping control which parts of the DNA are transcribed. DNA was first isolated by Friedrich Miescher in 1869, its molecular structure was first identified by Francis Crick and James Watson at the Cavendish Laboratory within the University of Cambridge in 1953, whose model-building efforts were guided by X-ray diffraction data acquired by Raymond Gosling, a post-graduate student of Rosalind Franklin. DNA is used by researchers as a molecular tool to explore physical laws and theories, such as the ergodic theorem and the theory of elasticity; the unique material properties of DNA have made it an attractive molecule for material scientists and engineers interested in micro- and nano-fabrication. Among notable advances in this field are DNA origami and DNA-based hybrid materials. DNA is a long polymer made from repeating units called nucleotides.
The structure of DNA is dynamic along its length, being capable of coiling into tight loops and other shapes. In all species it is composed of two helical chains, bound to each other by hydrogen bonds. Both chains are coiled around the same axis, have the same pitch of 34 angstroms; the pair of chains has a radius of 10 angstroms. According to another study, when measured in a different solution, the DNA chain measured 22 to 26 angstroms wide, one nucleotide unit measured 3.3 Å long. Although each individual nucleotide is small, a DNA polymer can be large and contain hundreds of millions, such as in chromosome 1. Chromosome 1 is the largest human chromosome with 220 million base pairs, would be 85 mm long if straightened. DNA does not exist as a single strand, but instead as a pair of strands that are held together; these two long strands coil in the shape of a double helix. The nucleotide contains both a segment of the backbone of a nucleobase. A nucleobase linked to a sugar is called a nucleoside, a base linked to a sugar and to one or more phosphate groups is called a nucleotide.
A biopolymer comprising multiple linked nucleotides is called a polynucleotide. The backbone of the DNA strand is made from alternating sugar residues; the sugar in DNA is 2-deoxyribose, a pentose sugar. The sugars are joined together by phosphate groups that form phosphodiester bonds between the third and fifth carbon atoms of adjacent sugar rings; these are known as the 3′-end, 5′-end carbons, the prime symbol being used to distinguish these carbon atoms from those of the base to which the deoxyribose forms a glycosidic bond. When imagining DNA, each phosphoryl is considered to "belong" to the nucleotide whose 5′ carbon forms a bond therewith. Any DNA strand therefore has one end at which there is a phosphoryl attached to the 5′ carbon of a ribose and another end a
Salvation
Salvation is being saved or protected from harm or being saved or delivered from a dire situation. In religion, salvation is the saving of the soul from its consequences; the academic study of salvation is called soteriology. In religion, salvation is the saving of the soul from its consequences, it may be called "deliverance" or "redemption" from sin and its effects. Salvation is considered to be caused either by the grace of a deity. Religions emphasize the necessity of both personal effort—for example and asceticism—and divine action. In contemporary Judaism, refers to God redeeming the people of Israel from their various exiles; this includes the final redemption from the present exile. Judaism holds. Jews do not subscribe to the doctrine of original sin. Instead, they place a high value on individual morality as defined in the law of God — embodied in what Jews know as the Torah or The Law, given to Moses by God on biblical Mount Sinai. In Judaism, salvation is related to the idea of redemption, a saving from the states or circumstances that destroy the value of human existence.
God, as the universal spirit and Creator of the World, is the source of all salvation for humanity, provided an individual honours God by observing his precepts. So redemption or salvation depends on the individual. Judaism stresses that salvation cannot be obtained through anyone else or by just invoking a deity or believing in any outside power or influence; the Jewish concept of Messiah visualises the return of the prophet Elijah as the harbinger of one who will redeem the world from war and suffering, leading mankind to universal brotherhood under the fatherhood of one God. The Messiah is not considered as a future divine or supernatural being but as a dominating human influence in an age of universal peace, characterised by the spiritual regeneration of humanity. In Judaism, salvation is not limited to those of the Jewish faith; when Jews refer to themselves as the chosen people of God, they do not imply they have been chosen for special favours and privileges but rather they have taken it upon themselves to show to all peoples by precept and example the ethical way of life.
When examining Jewish intellectual sources throughout history, there is a spectrum of opinions regarding death versus the afterlife. An over-simplification, one source says salvation can be achieved in the following manner: Live a holy and righteous life dedicated to Yahweh, the God of Creation. Fast and celebrate during the appropriate holidays. By origin and nature, Judaism is an ethnic religion. Therefore, salvation has been conceived in terms of the destiny of Israel as the elect people of Yahweh, the God of Israel. In the biblical text of Psalms, there is a description of death, when people go into the earth or the "realm of the dead" and cannot praise God; the first reference to resurrection is collective in Ezekiel's vision of the dry bones, when all the Israelites in exile will be resurrected. There is a reference to individual resurrection in the Book of Daniel, the last book of the Hebrew Bible, it was not until the 2nd century BCE that there arose a belief in an afterlife, in which the dead would be resurrected and undergo divine judgment.
Before that time, the individual had to be content that his posterity continued within the holy nation. The salvation of the individual Jew was connected to the salvation of the entire people; this belief stemmed directly from the teachings of the Torah. In the Torah, God taught his people sanctification of the individual. However, he expected them to function together and be accountable to one another; the concept of salvation was tied to that of restoration for Israel. During the Second Temple Period, the Sadducees, High Priests, denied any particular existence of individuals after death because it wasn't written in the Torah, while the Pharisees, ancestors of the rabbis, affirmed both bodily resurrection and immortality of the soul, most based on the influence of Hellenistic ideas about body and soul and the Pharisaic belief in the Oral Torah; the Pharisees maintained that after death, the soul is connected to God until the messianic era when it is rejoined with the body in the land of Israel at the time of resurrection.
According to the Gospel of John, Jesus said "salvation is from the Jews." This is in accordance with the Jewish concept of salvation, is a possible reference to Isaiah 49:6. Christianity’s primary premise is that the incarnation and death of Jesus Christ formed the climax of a divine plan for humanity’s salvation; this plan was conceived by God consequent on the Fall of Adam, the progenitor of the human race, it would be completed at the Last Judgment, when the Second Coming of Christ would mark the catastrophic end of the world. For Christianity, salvation is only possible through Jesus Christ. Christians believe that Jesus' death on the cross was the once-for-all sacrifice that atoned for the sin of humanity; the Christian religion, though not the exclusive possessor of the idea of redemption, has given to it a special definiteness and a dominant position. Taken in its widest sense, as deliverance from dangers and ills in general, mos
Precipitation (chemistry)
Precipitation is the creation of a solid from a solution. When the reaction occurs in a liquid solution, the solid formed is called the'precipitate'; the chemical that causes the solid to form is called the'precipitant'. Without sufficient force of gravity to bring the solid particles together, the precipitate remains in suspension. After sedimentation when using a centrifuge to press it into a compact mass, the precipitate may be referred to as a'pellet'. Precipitation can be used as a medium; the precipitate-free liquid remaining above the solid is called the'supernate' or'supernatant'. Powders derived from precipitation have historically been known as'flowers'; when the solid appears in the form of cellulose fibers which have been through chemical processing, the process is referred to as regeneration. Sometimes the formation of a precipitate indicates the occurrence of a chemical reaction. If silver nitrate solution is poured into a solution of sodium chloride, a chemical reaction occurs forming a white precipitate of silver chloride.
When potassium iodide solution reacts with lead nitrate solution, a yellow precipitate of lead iodide is formed. Precipitation may occur. Precipitation may occur from a supersaturated solution. In solids, precipitation occurs if the concentration of one solid is above the solubility limit in the host solid, due to e.g. rapid quenching or ion implantation, the temperature is high enough that diffusion can lead to segregation into precipitates. Precipitation in solids is used to synthesize nanoclusters. An important stage of the precipitation process is the onset of nucleation; the creation of a hypothetical solid particle includes the formation of an interface, which requires some energy based on the relative surface energy of the solid and the solution. If this energy is not available, no suitable nucleation surface is available, supersaturation occurs. Precipitation reactions can be used for making pigments, removing salts from water in water treatment, in classical qualitative inorganic analysis.
Precipitation is useful to isolate the products of a reaction during workup. Ideally, the product of the reaction is insoluble in the reaction solvent. Thus, it precipitates. An example of this would be the synthesis of porphyrins in refluxing propionic acid. By cooling the reaction mixture to room temperature, crystals of the porphyrin precipitate, are collected by filtration: Precipitation may occur when an antisolvent is added, drastically reducing the solubility of the desired product. Thereafter, the precipitate may be separated by filtration, decanting, or centrifugation. An example would be the synthesis of chromic tetraphenylporphyrin chloride: water is added to the DMF reaction solution, the product precipitates. Precipitation is useful in purifying products: crude bmim-Cl is taken up in acetonitrile, dropped into ethyl acetate, where it precipitates. Another important application of an antisolvent is in ethanol precipitation of DNA. In metallurgy, precipitation from a solid solution is a useful way to strengthen alloys.
An example of a precipitation reaction: Aqueous silver nitrate is added to a solution containing potassium chloride, the precipitation of a white solid, silver chloride, is observed. AgNO 3 + KCl ⟶ AgCl ↓ + KNO 3 The silver chloride has formed a solid, observed as a precipitate; this reaction can be written emphasizing the dissociated ions in a combined solution. This is known as the ionic equation. Ag + + NO 3 − + K + + Cl − ⟶ AgCl ↓ + K + + NO 3 − A final way to represent a precipitate reaction is known as a net ionic reaction. Many compounds containing metal ions produce precipitates with distinctive colors; the following are typical colors for various metals. However, many of these compounds can produce colors different from those listed. Other compounds form white precipitates. Precipitate formation is useful in the detection of the type of cation in a salt. To do this, an alkali first reacts with the unknown salt to produce a precipitate, the hydroxide of the unknown salt. To identify the cation, the color of the precipitate and its solubility in excess are noted.
Similar processes are used in sequence – for example, a barium nitrate solution will react with sulfate ions to form a solid barium sulfate precipitate, indicating that it is that sulfate ions are present. Digestion, or precipitate ageing, happens when a freshly formed precipitate is left at a higher temperature, in the solution from which it precipitates, it results in bigger particles. The physico-chemical process underlying digestion is called Ostwald ripening. Coprecipitation Salting in Salting out Effervescence Zumdahl, Steven S.. Chemical Principles. New York: Houghton Mifflin. ISBN 0-618-37206-7. Precipitation reactions of certain cations Digestion Instruments A Thesis on pattern formation in precipitation reactions
Solvatochromism
Solvatochromism is the phenomenon observed when the colour due to a solute is different when that solute is dissolved in different solvents. The solvatochromic effect is the way the spectrum of a substance varies when the substance is dissolved in a variety of solvents. In this context, the dielectric constant and hydrogen bonding capacity are the most important properties of the solvent. With various solvents there is a different effect on the electronic ground state and excited state of the solute, so that the size of energy gap between them changes as the solvent changes; this is reflected in the absorption or emission spectrum of the solute as differences in the position and shape of the spectroscopic bands. When the spectroscopic band occurs in the visible part of the spectrum solvatochromism is observed as a change of colour; this is illustrated by Reichardt's dye. Negative solvatochromism corresponds to a hypsochromic shift with increasing solvent polarity. An examples of negative solvatochromism is provided by 4--N-methylpyridinium iodide, red in 1-propanol, orange in methanol, yellow in water.
Positive solvatochromism corresponds to a bathochromic shift with increasing solvent polarity. An example of positive solvatochromism is provided by 4,4'-bisfuchsone, orange in toluene, red in acetone; the main value of the concept of solvatochromism is the context it provides to predict colors of solutions. Solvatochromism can in principle be used in sensors and in molecular electronics for construction of molecular switches. Solvatochromic dyes are used to measure solvent parameters, which can be used to explain solubility phenomena and predict suitable solvents for particular uses. Solvatochromism of the photoluminescence/fluorescence of carbon nanotubes has been identified and used for optical sensor applications. In one such application, the wavelength of the fluorescence of peptide-coated carbon nanotubes was found to change when exposed to explosives, facilitating detection. However, more the small chromophore solvatochromism hypothesis has been challenged for carbon nanotubes in light of older and newer data showing electrochromic behavior.
These and other observations regarding non-linear processes on the semiconducting nanotube suggest colloidal models will require new interpretations that are in line with classic semiconductor optical processes, including electrochemical processes, rather than small molecule physical descriptions. Conflicting hypotheses may be due to the fact the nanotube is only a single atom thick material interface unlike other "bulk" nanomaterials. Negative solvatochromism experiment Positive solvatochromism experiment
Negative number
In mathematics, a negative number is a real number, less than zero. Negative numbers represent opposites. If positive represents a movement to the right, negative represents a movement to the left. If positive represents above sea level negative represents below sea level. If positive represents a deposit, negative represents a withdrawal, they are used to represent the magnitude of a loss or deficiency. A debt, owed may be thought of as a negative asset, a decrease in some quantity may be thought of as a negative increase. If a quantity may have either of two opposite senses one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. In the medical context of fighting a tumor, an expansion could be thought of as a negative shrinkage. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature; the laws of arithmetic for negative numbers ensure that the common sense idea of an opposite is reflected in arithmetic.
For example, − = 3 because the opposite of an opposite is the original value. Negative numbers are written with a minus sign in front. For example, −3 represents a negative quantity with a magnitude of three, is pronounced "minus three" or "negative three". To help tell the difference between a subtraction operation and a negative number the negative sign is placed higher than the minus sign. Conversely, a number, greater than zero is called positive; the positivity of a number may be emphasized by placing a plus sign before it, e.g. +3. In general, the negativity or positivity of a number is referred to as its sign; every real number other than zero is either negative. The positive whole numbers are referred to as natural numbers, while the positive and negative whole numbers are referred to as integers. In bookkeeping, amounts owed are represented by red numbers, or a number in parentheses, as an alternative notation to represent negative numbers. Negative numbers appeared for the first time in history in the Nine Chapters on the Mathematical Art, which in its present form dates from the period of the Chinese Han Dynasty, but may well contain much older material.
Liu Hui established rules for subtracting negative numbers. By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers. Islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients. Western mathematicians accepted the idea of negative numbers around the middle of the 19th century. Prior to the concept of negative numbers, mathematicians such as Diophantus considered negative solutions to problems "false" and equations requiring negative solutions were described as absurd; some mathematicians like Leibniz agreed that negative numbers were false, but still used them in calculations. Negative numbers can be thought of as resulting from the subtraction of a larger number from a smaller. For example, negative three is the result of subtracting three from zero: 0 − 3 = −3. In general, the subtraction of a larger number from a smaller yields a negative result, with the magnitude of the result being the difference between the two numbers.
For example, 5 − 8 = −3since 8 − 5 = 3. The relationship between negative numbers, positive numbers, zero is expressed in the form of a number line: Numbers appearing farther to the right on this line are greater, while numbers appearing farther to the left are less, thus zero appears in the middle, with the positive numbers to the right and the negative numbers to the left. Note that a negative number with greater magnitude is considered less. For example though 8 is greater than 5, written 8 > 5negative 8 is considered to be less than negative 5: −8 < −5. It follows that any negative number is less than any positive number, so −8 < 5 and −5 < 8. In the context of negative numbers, a number, greater than zero is referred to as positive, thus every real number other than zero is either positive or negative, while zero itself is not considered to have a sign. Positive numbers are sometimes written with a plus sign in front, e.g. +3 denotes a positive three. Because zero is neither positive nor negative, the term nonnegative is sometimes used to refer to a number, either positive or zero, while nonpositive is used to refer to a number, either negative or zero.
Zero is a neutral number. Goal difference in association football and hockey. Plus-minus differential in ice hockey: the difference in total goals scored for the team and against the team when a particular player is on the ice is the player’s +/− rating. Players can have a negative rating. Run differential in baseball: the run differential is negative if the team allows more runs than they scored. British football clubs are deducted points if they enter administration, thus have a negative points total until they have earned at least that many points that season. Lap times in Formula 1 may be given as the difference compared to a previous lap, will be positive if slower and negative if faster. In some athletics events, such as sprint races, the hurdles, the triple jump and the long jump, the wind assistance is measured and recorde
