Is there a math symbol that stands for becomes?

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Discussion Overview

The discussion revolves around the search for a mathematical symbol that represents the concept of "becomes." Participants explore various notations and their contexts, including function mapping and implications, while considering how these symbols might be applied in specific problems.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses curiosity about a symbol for "becomes" that could aid in solving problems.
  • Another participant suggests barred arrow notation, explaining its use in mapping functions, exemplified by x \mapsto x^2 + 4.
  • Some participants propose using \Longrightarrow or \Rightarrow as potential symbols for "becomes."
  • There is a request for concrete examples to clarify the intended use of the symbol.
  • One participant mentions that the side arrow might be appropriate but warns it could be an abuse of notation depending on the context.
  • Another participant introduces the tilde symbol (~) as representing "becomes asymptotically equal to," providing a mathematical context for its use.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a specific symbol for "becomes," and multiple competing views on appropriate notations remain. The discussion is open-ended with requests for examples to further clarify the topic.

Contextual Notes

Some limitations exist regarding the definitions and contexts of the proposed symbols, as well as the potential for notation abuse depending on their application.

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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