In geometry, $\cong$ means congruence of figures, which means the figures have the same shape and size. (In advanced geometry, it means one is the image of the other under a mapping known as an "isometry", which provides a formal definition of what "same shape and size" means) Two congruent triangles look exactly the same, but they are not the ...

$\cong$ is used to show a congruency between two mathematical expressions, which could be geometrical, topological, and when using modulo arithmetic you can get different numbers that are congruent, e.g., $5 \text{ mod } 3 \cong 11 \text{ mod } 3$ (although this is also written as $\equiv$). In LaTeX it is coded as \cong.

Jan 1, 2025 · I went through several pages on the web, each of which asserts that $\operatorname{Aut} A_n \cong \operatorname{Aut} S_n \; (n\geq 4)$ or an equivalent statement without proof, and many of them seem to regard it as a trivial fact.

Aug 22, 2023 · Q1: Yes, this is the definition of the determinant of a one-dimensional vector space. Q2: Yes, the dual of the trivial line bundle is the trivial line bundle (for instance, use that a line bundle is trivial iff it has a non-vanishing global section).

Nov 28, 2014 · How can I see that the connected sum $\\mathbb{P}^2 \\# \\mathbb{P}^2$ of the projective plane is homeomorphic to the Klein bottle? I'm not necessarily looking for an explicit homeomorphism, just an

There are a couple of questions from about a year ago in a similar vein to this one on math.SE. So I thought it would be useful to post this answer linking to two of them and relating them to your question.

May 28, 2017 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

$\begingroup$ This is an old question which already has an accepted answer which seems to be pretty clear. I'm not sure what the link that you give above adds to the conversation, and the brief explanation you provide does little to clarify.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.