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The symbol ≅ is used for isomorphism of objects of a category, and in particular for isomorphism of categories (which are objects of cat) “it depends on the user whether an approximation is sufficiently good. The symbol ≃ is used for equivalence of categories

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At least, this is the convention used in this book and by most category theorists, although it is far from universal in mathematics at large. This is an intentionally vague relation ≈ indicates a value which can be considered functionally equivalent for a calculation within an acceptable degree of error, whereas ~ is usually used to indicate a larger, possibly.

I have been wondering for a long time whether there is a unequivocal way to define and use the symbols commonly adopted for an approximate equality between two quantities

I am a physicist, and i o. Symbol ask question asked 6 years, 10 months ago modified 6 years, 10 months ago Probably because it is faster to write $\sim$ than $\approx$ Here is an example for proportionality

$$\text {number of steaks}\sim\text {number of cows},$$ meaning the number of steaks is proportional (proportionally growing) with the number of cows. It also is built from the symbols $<$ (less than) and $\approx$ (approximately equal) in the very same way as $\leqq$ (less or equal) is built from $<$ (less) and $=$ (equal). To indicate approximate equality, one can use ≃, ≅, ~, ♎, or ≒ I need to indicate an approximate inequality

Specifically, i know a is greater than a quantity of approximately b

Is there a way to I suppose similarity is an equivalence relation $\equiv$ is equivalent to and appears in regularly in modular arithmetic $\cong$ is congruence or isomorphism.

The $\approx$ symbol and the $ \fallingdotseq $ symbol both have the same denotation to generally mean approximately, with the latter symbol commonly used throughout some asian countries like japan and korea. The symbol u+2248 “≈” denotes, according to the standard, the relation “is approximately equal to”