What's the difference between "≡" ("identical to") and "≣" ("strictly equivalent to")?
"Strictly equivalent to" ("≣") is UTF character 2263, classified in the Mathematical Operators block.
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1I never heard of "≣" ("strictly equivalent to"). Where did it occur? – marty cohen May 20 '18 at 3:36
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9Ditto. Never heard of the four-bar version. Unless it means you have a good Wi-Fi signal. – user4894 May 20 '18 at 3:37
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@martycohen It's UTF character 2263. See the link I added to my answer. – Geremia May 20 '18 at 3:46
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2this looks more like a Unicode question, rather than a math question. might be the unicode people had a slot for a character in which they didn't know what to put, or had some leftover bars to dispose of. – Mirko May 20 '18 at 3:51
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3and similar variations are a generic symbols used to notate an equivalence relation. is the specific equivalence relation "equals" that we are used to with sets and natural numbers and by extension is also the symbol used for equality of rational, real, complex numbers etc... For more information on the definition of a specific equivalence relation, you will need to provide information about that specific equivalence relation. There are too many to provide the definitions of every one. – JMoravitz May 20 '18 at 3:52
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Let's say you have two expressions and . A way of expressing that they are equivalent, or equal to each other by definition, is as follows:
However, the symbol also denotes congruence, e.g. , so using the symbol for two different circumstances can cause some confusion. Thus, to denote , some write that
But, there is also another (but less common) variation, namely,
The "quadruple bar" is not used to denote congruence.
This post might serve useful.
