Is there a math symbol that stands for becomes?

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The discussion centers on the search for a mathematical symbol that represents the concept of "becomes." Participants suggest using barred arrow notation, specifically the expression x \mapsto x^2 + 4, which denotes the mapping of x to a new value. Additionally, symbols like \Longrightarrow and \Rightarrow are mentioned, with the latter typically indicating implication rather than transformation. The tilde symbol (~) is also noted for its use in denoting asymptotic equivalence, particularly in limits.

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TrevorRyan
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Just curious because it would really work into a few problems I am doing
 
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What is the context?
Barred arrow notation shows the result of applying a function to the object on the left of the arrow. An example would be:
x \mapsto x^2 + 4
which is read as "x is mapped to x squared plus 4."
 
How about \Longrightarrow \text { or } \Rightarrow ?
 
TrevorRyan said:
Just curious because it would really work into a few problems I am doing

Got any concrete example??
 
micromass said:
Got any concrete example??
Yeah, show us what you want to use it for.
I put in another vote for when f:X\to Y, then for any x\in X,

x\mapsto y, where y\in Y.

This is for elements. Bob S's version may be better for statements. But if you show us an example, we can be sure that we mean what we mean.
 
I would go with the side arrow, although depending on what you're using it for, it may be an abuse of notation. I usually go with the style of arrow Bob S suggested, although I think it means "implies" if you're strictly adhering to convention.
 
The tilde symbol ~ can mean "becomes asymptotically equal to", e.g. f(x) ~ g(x) \Rightarrow \lim_{x \rightarrow \infty} \frac{f(x)}{g(x)} = 1.
 

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