The approximation sign "≈" I use for decimal approximations with tilde "~" being a rougher approximation. Tilde "~" I use to state a geometric shape is similar to another one ie a triangle of sides 3/4/5 is similar to a triangle with sides 30/40/50. I write ABC ~ A'B'C' where A'B'C' is a dilated version of the pre-image.

Sep 1, 2014 · Congruent figures have the same shape and size (informally) but possibly different points. No diagram is needed for this explanation. Part of the confusion between "equal" and "congruent" probably comes from the fact that congruence is an equivalence relation .

In mathematics, it is useful to make a distinction between the two concepts: indiscernible (i.e. congruent) triangles may occupy different parts of space, for example, and isomorphic groups may need to be distinguished if, say, we are dealing with them as part of a larger problem or situation in which we need to deal with more than just their ...

Aug 14, 2015 · But I use both equal ($=$) and congruent to ($\equiv$) signs together when processing a lengthy calculation in modular arithmetic. My freshman algebra students quickly catch on with my calculations like $$ 12^{3004}\equiv5^{3004}=5^{3000}\cdot 5^4=(5^6)^{500}\cdot 5^4\equiv 1^{500}\cdot5^4=25^2\equiv4^2=16\equiv2\pmod7. $$ IOW, I …

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Nov 13, 2015 · A symbol I have in my math homework looks like a ~ above a =. (That is, $\cong$.) What does this mean? I'm studying Congruency at the moment if that helps.

Oct 21, 2013 · I'm reading up on Wilson's Theorem, and see a symbol I don't know... what does an equal sign with three lines mean? I'm looking at the example table and I still can't infer what they are trying to...

In an Introduction to Abstract Algebra by Thomas Whitelaw, he gives examples of the congruence mod operation, such as $13 \\equiv5 \\pmod4$, and $9 \\equiv -1 \\pmod 5$. But when I first learned about...

Sep 28, 2013 · According to it, U+2245 “≅” denotes the relations “is congruent to” and “is isomorphic to” for point sets (geometrical figures), and it is also used “for isomorphisms of mathematical structures”. So it has nothing to do with numerical approximations, for example.

Oct 30, 2021 · First, it should be written as $\;7\equiv 2\pmod 5$. It is read as ‘$7$ is congruent to $2$ modulo $5$’. It simply means that $7$ and $2$ have the same remainder when divided by $5$. $\endgroup$ –