2017年6月30日 · Wikipedia says that- The triple bar symbol is also sometimes used in place of an equal sign for equations that define the symbol on the left-hand side of the equation, to contrast them with equations in which the terms on both sides of the equation were already defined. Someone please explain the highlighted statement with few examples?

2012年3月23日 · In the first page of Disquisitiones Arithmeticae Gauss says that he has adopted this symbol from Legendre but Legendre used this symbol to show both equality and congruence while Gauss uses this symbol only for congruence to distinguish it from equality. Anyway, I don't think that this symbol is meant to be used for 'is defined as' naturally.

2015年10月30日 · The usage of the second triple bar is not correct, because you neither use $\sin$ and $\cos$ to define $1$ (the definition $1 :\equiv \sin^2(x) + \cos^2(x)$ is completely nonsensical), nor the other way round (the definition $\sin^2(x) + \cos^2(x) :\equiv 1$ would be even more absurd).

2015年10月4日 · $\begingroup$ But the Unicode character ≡, U+2261, has the name “identical to”. On the other hand, the quadruple bar one, ≣, U+2263, has the name “strictly equivalent to”, although I don’t what to think about the “strictly” in the name, especially that there seems to not be any “equivalent to” for short.

2018年5月20日 · $\begingroup$ $\equiv$ and 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...

2006年2月19日 · In summary, A,B| A = B is a notation used in mathematical logic to represent a logical statement where A and B are given as assumptions and the triple bar symbol (≡) denotes logical equivalence. To prove A = B means to show that A and B are logically equivalent, which can be done using logical rules and reasoning.

2010年6月10日 · If you have the 2007 version of word, you can go in 'insert' and then insert an equation which you can then format to get the bar above, if not you might have to stick to using '1/λ' or just 'v'. As for the triple bond, you can copy & paste this '≡'.

2019年5月27日 · I keep seeing this symbol $\\equiv$ in Mathematical Analysis -1, Zorich. What does it mean? For example: in page 180 we have, Some other pages it occurs in: 117, 139.

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I'm a bit pluzzled with the notation and can't find a concrete explanation on the internet. I know the triple bar symbol means "identical equality between two functions", but I don't how "def" changes its meaning. Moreover, I don't get what the "delta hat", and the h and k (they weren't defined before) have to do here.