Symbols Used by Mathematicians - What is a Vertical Bar with an Arrow?

[db1uover]

What symbol is a small vertical bar with an arrow? I know a plain arrow is "determines". Is there a good site that lists the vocabulary of mathematicians?

 

[symbolipoint]

If you exactly mean that description as a mathematical symbol, I'm not sure; but (assuming the arrow head points upward) if it's a text symbol used in computer programming, your description would mean "exponentiation"; if your symbol is actually used in writing chemical reactions, it would mean "as a gas" when written to the right-hand side of a chemical compound.

 

[tiny-tim]

What symbol is a small vertical bar with an arrow? I know a plain arrow is "determines". Is there a good site that lists the vocabulary of mathematicians?

Hi db1uover!

Do you mean \uparrow ?

If so, I think it only means "spin-up" (for spinors).

btw, if you're really into symbols, bookmark http://www.physics.udel.edu/~dubois/lshort2e/node61.html#SECTION008100000000000000000

 

[Hootenanny]

Alternatively, the symbol \mapsto means "maps to" and is used when defining functions and performing http://en.wikipedia.org/wiki/Map_(mathematics)"

 

[db1uover]

Thank you all. Hootenanny, that is what I was looking for, the mathematical verbage. So, the difference between 'maps to' and 'determines' is one is already in place while the other is being fleshed out?

 

[cristo]

Thank you all. Hootenanny, that is what I was looking for, the mathematical verbage. So, the difference between 'maps to' and 'determines' is one is already in place while the other is being fleshed out?

Not sure what you are asking, but the difference between \to and \mapsto is best described by an example. So, say, the real function f(x)=x^2 would be expressed as f:\mathbb{R}\to\mathbb{R}, x\mapsto x^2

 

[db1uover]

So, say, the real function f(x)=x^2 would be expressed as f:\mathbb{R}\to\mathbb{R}, x\mapsto x^2

Is this read as 'function f such that Real determines Real when x maps to x squared'? I'm out of school, but trying to remember standard math-ese.

 

[Hurkyl]

I've also seen that symbol used to refer to injections. e.g. Rather than write X \to Y, you write X \mapsto Y to state that the map is actually monic.

 

[CRGreathouse]

Is this read as 'function f such that Real determines Real when x maps to x squared'? I'm out of school, but trying to remember standard math-ese.

I read it as "a function f from the reals to the reals that maps x to x squared", or more likely "a function f from R to R that maps x to x squared".

I haven't seen it used in Hurkyl's sense.