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Math Help - "Maps to"

  1. #1
    Member Greengoblin's Avatar
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    "Maps to"

    Wasn't sure where to put this, but what is the difference between the symbols \mapsto and \rightarrow ? I have seen the former a few times, and it seems to be in a similar context to the lattter, but is there actually a difference?
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  2. #2
    MHF Contributor
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    In all texts I've read, I've only seen the latter used. I can't clear things up really, just wanted to tell you that. I wouldn't be surprised if they meant the same thing and I wouldn't be surprised if they were very different. That's math for you
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  3. #3
    Moo
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    Hello,

    Usually, we can see the two used at the same time in this type of things :

    f(x)=x^2 can be written this way :

    \begin{aligned} f ~:~ & \mathbb{R} & \to & ~\mathbb{N} \hfill \\ & x & \mapsto & ~x^2 \hfill \end{aligned}

    The \to is to define the domains, in which range does the domain "maps to"
    The \mapsto is to define by which value a number will be associated. "maps to" too.

    All the time I've seen the two, \to was used for the domain/range and \mapsto was used for associating a value to a number.

    I don't know if you can see the difference with this example... ?
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  4. #4
    Member Greengoblin's Avatar
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    Yeh thanks Moo, I can see the difference between the two. Although looking through some peoples use of them on this forum, they seem to just use them interchangeably. I guess \mapsto is quicker to write than \rightarrow.
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