Is there a math symbol that stands for becomes?

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In summary, the conversation discusses different notations used to express the result of applying a function to an object. The barred arrow notation and the side arrow notation are mentioned and it is noted that the tilde symbol can also be used in certain contexts. Concrete examples are requested to clarify the meaning of these notations. The conversation also touches on the potential ambiguity and connotations of each notation.
  • #1
TrevorRyan
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Just curious because it would really work into a few problems I am doing
 
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  • #2
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:
[tex]x \mapsto x^2 + 4[/tex]
which is read as "x is mapped to x squared plus 4."
 
  • #3
How about [itex] \Longrightarrow \text { or } \Rightarrow [/itex] ?
 
  • #4
TrevorRyan said:
Just curious because it would really work into a few problems I am doing

Got any concrete example??
 
  • #5
micromass said:
Got any concrete example??
Yeah, show us what you want to use it for.
I put in another vote for when [itex]f:X\to Y[/itex], then for any [itex]x\in X[/itex],

[itex]x\mapsto y[/itex], where [itex]y\in Y[/itex].

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.
 
  • #6
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.
 
  • #7
The tilde symbol ~ can mean "becomes asymptotically equal to", e.g. [itex]f(x)[/itex] ~ [itex]g(x) \Rightarrow \lim_{x \rightarrow \infty} \frac{f(x)}{g(x)} = 1[/itex].
 

What is the math symbol that stands for "becomes"?

The math symbol that stands for "becomes" is an equal sign with an arrow on top, which looks like this: →

Can the symbol for "becomes" be used in all math operations?

Yes, the symbol for "becomes" can be used in all math operations, as it represents a transformation or change in value.

Is the symbol for "becomes" commonly used in algebraic equations?

Yes, the symbol for "becomes" is commonly used in algebraic equations, particularly to represent a variable's value changing over time or in a sequence.

Can the symbol for "becomes" be used in both positive and negative changes?

Yes, the symbol for "becomes" can be used in both positive and negative changes, as it simply indicates a change in value, regardless of the direction.

Are there any other symbols that can be used to represent "becomes"?

Yes, there are other symbols that can be used to represent "becomes," such as the delta symbol (Δ) or the notation ":=." However, the equal sign with an arrow on top is the most commonly used symbol for "becomes."

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