![]() Approximations might also be used if incomplete information prevents use of exact representations. ![]() An approximate model is used to make calculations easier. In science, approximation can refer to using a simpler process or model when the correct model is difficult to use. The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct similar, but not exactly the same (e.g., the approximate time was 10 o'clock).Īlthough approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws. ![]() In everyday English, words such as roughly or around are used with a similar meaning. Words like approximate, approximately and approximation are used especially in technical or scientific contexts. The word approximation is derived from Latin approximatus, from proximus meaning very near and the prefix ad- ( ad- before p becomes ap- by assimilation) meaning to. ![]() JSTOR ( April 2013) ( Learn how and when to remove this template message)Īn approximation is anything that is intentionally similar but not exactly equal to something else.Unsourced material may be challenged and removed. Please help improve this article by adding citations to reliable sources. These symbols more commonly have one end closed with the other end open, suggesting which side is "bigger.This article needs additional citations for verification. Similarly to how there are many symbols for equivalence relations ( or equivalence-like relations) in use, there are many different symbols for orders and partial orders, such as $<,\leq,\prec,\preceq,\subset,\subseteq\dots$, again with some orders exclusively using one symbol over another but symbols being used for multiple things. ( Note that this example is not an equivalence relation since the relation is not transitive., $9.82\not\approx 10.47$).Īs for what the symbols are named, I am in the habit of either referring to them by the name of the relation they are being used to represent, or referring to them by their $\LaTeX$ designation ($\simeq$ being called "simeq" for example) Here we would have something like $10.47\approx 10$ and also $9.82\approx 10$. For example $\approx$ might represent the relation " is close in value to" where we say for example $a\approx b$ iff $|a-b|<0.5$. There are some situations where those symbols which have squiggles may be used to represent relations which are not true equivalence relations, but act similarly to equivalence relations. On the other hand, most if not all symbols in that list can be used for multiple different situations, such as how we use $=$ to represent equality between real numbers, equality between matrices, equality between sets, etc. ![]() On the other hand, some equivalence relations do not have a universally designated symbol to use, so any from that list ( or similar to those in that list) may be used and is largely author preference. Some specific equivalence relations may have standard choices for which symbol to use ( such as how our usual equality is almost always represented by $=$). Symbols such as $\sim,\approx,\simeq,\approxeq,=,\equiv,\fallingdotseq,\risingdotseq,\doteqdot,\dots$ where lines are generally parallel or squiggles generally represent equivalence relations. ![]()
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