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Another possible notation for the same relation is {\displaystyle A\ni x,} A\ni x, meaning "A contains x", though it is used less often. The negation of set membership is denoted by the symbol "∉". Writing {\displaystyle x\notin A} x\notin A means that "x is not an element of A".
As said, A = B ⇐ A is even, or A = B if A is even works, but we can do it slightly differently too; "because" also means the same thing as "if" or "when": A = B ∵ A is even. Personally, I see " A = B if A is even " the most (and yes, I actually see this quite a bit; my professor likes to state theorems with "if"), and I like to explain why ...
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.
Please check the notation tag wiki for a link. It's also not uncommon to write something like "a<b,c" to indicate that "a<b and a<c". In my opinion, you should mostly write what's easiest for the reader to extract the meaning from. The logical "and" is ∧ ∧ (and the corresponding "or" is ∨ ∨).
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 ...
An finite ordered set of n n elements is called a n n -tuple, and is commonly denoted with parenthesis, e.g. (1, 2,..., 5) (1, 2,..., 5) for the 5-tuple of 1 to 5. But this notation clashes with open intervals, when working with 2-tuples. So you should probably add some explanatory text depending on who your target audience is.
f: x ↦ y means that f is a function which takes in a value x and gives out y. f: N → N means that f is a function which takes a natural number as domain and results in a natural number as the result. Because you're wrong: the → and ↦ arrows mean different things. Also, W is not the set of positive numbers: that's R +.
1. For example, 3 ∏ i = 0ai = a0 ⋅ a1 ⋅ a2 ⋅ a3. This is a symbol for product similarly as ∑ for sum. Your use of the × symbol begs the question, if the products are vectors is the pi-product scalar or vector? (cross or dot product) If it is not vector, then the ⋅ symbol would be more appropriate.
This notation means that you take the output of h h and use it as the input of f f. When we are working with a specific x x value, we can suggestively write f(h(x)) f (h (x)) instead. (f ∘ h)(x) = f(h(x)) = f(2 + 3x) = 1 2 + 3x. (f ∘ h) (x) = f (h (x)) = f (2 + 3 x) = 1 2 + 3 x. (Note: I only used z z as the variable for f f to avoid ...
what is the meaning of this symbol $ ∨?$ 1. What is the meaning of $\vartriangleleft$ symbol? 0