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The symbol ≅ is used for isomorphism of objects of a category, and in particular for isomorphism of categories (which are objects of CAT). The symbol ≃ is used for equivalence of categories. At least, this is the convention used in this book and by most category theorists, although it is far from universal in mathematics at large.
2014年6月25日 · I have started seeing the "∈" symbol in math. What exactly does it mean? I have tried googling it but google takes the symbol out of the search.
2020年11月17日 · I have some confusion in symbolics what is the meaning of this symbol $\\land?$ My attempt : I was googling and got the answer given below But i didn't understand the given above answer My confus...
26. The logical "and" is ∧ ∧ (and the corresponding "or" is ∨ ∨). Let me note that, unless you are actually talking about formal logic (or set theory, etc.), most people never use this symbol to mean "and" in "ordinary" mathematics.
That said, there are many places where symbols are useful and simplify matters. The word "where" can often be replaced with "such that", and corresponding to this we have a few regularly used symbols. For instance, in set builder notation the colon (or bar) is used to indicate a condition (read "where" or "such that"): {x ∈R: x> 0}. {x ∈ R ...
2014年11月3日 · If you want to keep them in the original order, you can write " A = B A = B if A A is even." This is semantically the same as the other answers. Of course, "if" is not a symbol per se, but it might as well be one, and it's a little clearer and more directly logical than "when". Share.
2011年3月18日 · y:= 7x + 2 y:= 7 x + 2. means that y y is defined to be 7x + 2 7 x + 2. This is different from, say, writing. 1 =sin2(θ) +cos2(θ) 1 = sin 2 (θ) + cos 2 (θ) where we are saying that the two sides are equal, but we are not defining "1" to be the expression " sin2(θ) +cos2(θ) sin 2 (θ) + cos 2 (θ) ". Basically, some people think that there ...
2015年8月19日 · In my opinion, a notation using Z Z (such as Z≥0 Z ≥ 0) is preferable over a notation using N N, a symbol that means different things in different countries. Z+ Z + looks like the set of strictly positive integers to me. N ∪ {0} N ∪ {0} is unambiguous, even if it is redundant ('cause, you know, 0 ∈N 0 ∈ N). Z⩾0 Z ⩾ 0 is also clear.
I know the "such that" symbol $\mid$ from the definition of sets: $$\{x \mid x \in \Bbb N \land x < 3\}$$ Is it OK to use this symbol outside of sets. For instance, if I want to define a function that takes a non-empty set of natural numbers and yields the least element of this set, can I write:
47. Element-wise product of matrices is known as the Hadamard product, and can be notated as A ∘ B A ∘ B. Some basic properties of the Hadamard Product are described in this section from an open source linear algebra text.
