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Q&A

What it ≡ called?

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I saw the text (≡) few times. When I had searched in internet I got that..

In mathematics, the triple bar is sometimes used as a symbol of identity or an equivalence relation (although not the only one; other common choices include ~ and ≈).[7][8] Particularly, in geometry, it may be used either to show that two figures are congruent or that they are identical.[9] In number theory, it has been used beginning with Carl Friedrich Gauss (who first used it with this meaning in 1801) to mean modular congruence: {\displaystyle a\equiv b{\pmod {N}}}a \equiv b \pmod N if N divides a − b.[10][11] It is also used for "identical equality" of functions; one writes {\displaystyle f\equiv g}f \equiv g for two functions f, g if we have {\displaystyle f(x)=g(x)}f(x) = g(x) for all x ~ https://en.wikipedia.org/wiki/Triple_bar

I don't have any problem with understanding the "letter". But I was thinking what it actually called. Like as we call = it equal... plus, minus, proportional etc etc. But what it actually called? I don't think triple bar is meaningful cause $\bar{x}$ it's called bar x. But whenever we say triple bar seems like they are trying to represent something just like this but in reality there's no double or triple bar on above of $x$ but triple bar for that symbol isn't looking good to me. Is there anything else to call it?

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Is congruent to

This satisfies both usages you mentioned and is the most common way I pronounce it/hear it pronounced.

$8 \equiv 3 \pmod{5} \to \text{8 is congruent to 3 mod 5 }$ $\triangle ABC \equiv \triangle DEF \to \text{Triangle ABC is congruent to Triangle DEF}$

Alternatively, "is equivalent to" could work in most cases - in fact, the $\LaTeX$ command for this is $\text{\equiv}$.

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