# what is meaning of ^ symbol in math?

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Hi all! What is meaning of ^ symbol in math? Thanks for all help.

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It's used to represent exponentiation. So 2^2 means 22.

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In math, X ^ Y means X to the power of Y.

2 ^ 3 = 8

If you are using a programming language be wary that may C-like languages use ^ to represent the bitwise XOR operation.

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It can also be used as a hat above a symbol, which typically denotes a unit vector.

Thank you.

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Guys, I am not proud of you today! the ^ symbol has nothing to do with the exponential in mathematics.

The ^ symbol represent the logical conjunction, or more simply the logical "and".

Having ^ represent the exponential is not a mathematical convention, it is a text formatting shortcut, probably started by latex. In latex, when you want to superscript something, you use "^{blah}", and "_{blah}" to underscript. But "^" does NOT represent the exponential in mathematical language.

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Quote:
 Original post by SteadtlerThe ^ symbol represent the logical conjunction, or more simply the logical "and".

Don't confuse the wedge (which this forum apparently doesn't like) with the caret (^). The use of the latter to represent exponentiation goes back to ALGOL.

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Quote:
 Original post by SteadtlerGuys, I am not proud of you today! the ^ symbol has nothing to do with the exponential in mathematics.

It can mean that, in some contexts.

Quote:
 Original post by SteadtlerThe ^ symbol represent the logical conjunction exclusive disjunction, or more simply the logical "and" "xor".

Fixed.

Depending on the context, it can mean any of the things mentioned.

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Quote:
 Original post by SteadtlerGuys, I am not proud of you today! the ^ symbol has nothing to do with the exponential in mathematics... But "^" does NOT represent the exponential in mathematical language.
Actually ^ does have to do with exponents and math.

For instance, when you're first taught exponents in school, they wont use the superscript method - they'll use ^. Kind of like how they use the x for multiplication until you start using a dot. ^ is a very valid and widely accepted means to denote exponent.

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Quote:
 Original post by KimaniFor instance, when you're first taught exponents in school, they wont use the superscript method - they'll use ^. Kind of like how they use the x for multiplication until you start using a dot. ^ is a very valid and widely accepted means to denote exponent.

Maybe.

Teaching style varies just as much as notation does. That is: A lot.

There is no single answer to this. As Roboguy said, it depends on context.

John B

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Those are all programming syntax taken from different languages. Think as you wish, but if you were to write a science paper, and used ^ for anything else than logical conjunction in an equation, I would expect any serious publication to reject it.

And dont be tricked, while it means XOR in some programming languages, the actual math symbol for XOR is "ˇ". Because you know, most keyboards cannot conveniently type a "ˇ", and even then, its not very readable. The mathematical symbol for XOR dont seem to be in the ascii table so I cant type it. It normally is a circle with a straith cross inside.

[Edited by - Steadtler on June 5, 2007 1:25:17 PM]

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Quote:
 Original post by KimaniActually ^ does have to do with exponents and math.For instance, when you're first taught exponents in school, they wont use the superscript method - they'll use ^. Kind of like how they use the x for multiplication until you start using a dot. ^ is a very valid and widely accepted means to denote exponent.

Yeah, grade school teachers sucks at math. I had my head of department try to explain a bunch of them (actually they were high school) the difference between convex and concave - a painful hour according to him.

They use "*" for multiplication because thats whats on calculators. They wouldnt know that the star means a convolution because 99% of them dont know what a convolution is. And it woudlnt serve the kids because the dot is not on calculators. Its a case of leveling by the bottom...

Best forget most of the math you learned before college when you get there, it'll help you out.

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A friend of mine was told there was no such thing as negative numbers.

School rocks!

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Quote:
 Original post by SteadtlerThose are all programming syntax taken from different languages. Think as you wish, but if you were to write a science paper, and used ^ for anything else than logical conjunction in an equation, I would expect any serious publication to reject it.

If you were to write a science paper, and used ^ for exponentiation, I would expect any serious publication to consider it a typo. If you were to write a science paper, and used ^ for conjunction, I would expect any serious publication to consider it a typo.

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Quote:
 Original post by instinKtA friend of mine was told there was no such thing as negative numbers.School rocks!

Well, in the set of positive integer, there is no such thing :). In the set of positive real too! And in the set or positive rational...

number is such a loose word!

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When I see ^ in maths, it's either

cross product (most texts use X though)

set intersection (normally bigger wigwam though)

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Quote:
 Original post by SneftelIf you were to write a science paper, and used ^ for exponentiation, I would expect any serious publication to consider it a typo. If you were to write a science paper, and used ^ for conjunction, I would expect any serious publication to consider it a typo.

I did publish several science papers, but I never needed to use the conjunction symbol in my equations (I think), so I admit I dont know first hand. Why would they consider it a typo when it is the only correct mathematical symbol for conjunction? Im curious to what you use for conjunction if not it.

I cannot believe reading you guys, math is supposed to be the least ambiguous thing out there. The OP asked for the meaning of ^ in math, and I stand that it is the conjunction, and not any of the other meanings mentionned here.

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Quote:
 Original post by SteadtlerI did publish several science papers, but I never needed to use the conjunction symbol in my equations (I think), so I admit I dont know first hand. Why would they consider it a typo when it is the only correct mathematical symbol for conjunction? Im curious to what you use for conjunction if not it.

It's pissing me off because I can't seem to post the symbol here. Look here, and search the page for "∧" (without the quotes). It looks like the caret, but it's larger, lower, and more acute.

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Quote:
Original post by Sneftel
Quote:
 Original post by SteadtlerI did publish several science papers, but I never needed to use the conjunction symbol in my equations (I think), so I admit I dont know first hand. Why would they consider it a typo when it is the only correct mathematical symbol for conjunction? Im curious to what you use for conjunction if not it.

It's pissing me off because I can't seem to post the symbol here. Look here, and search the page for "∧" (without the quotes). It looks like the caret, but it's larger, lower, and more acute.

I see the symbol here, maybe its your language set. Anyway, the *only* similar math symbol to both those characters is still the conjunction symbol.

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Quote:
 Original post by SteadtlerI see the symbol here, maybe its your language set.
Yeh, now I see it on one of my computers but not the other.
Quote:
 Anyway, the *only* similar math symbol to both those characters is still the conjunction symbol.

Not true. In articles written in the days before TeX, and even these days in text-based circumstances, it's quite common to see ^ used for exponentiation. I've got some old Blinn papers in my filing cabinet at work that I'm almost certain use ^ in that way. It may be something which is specific to computer science literature.

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Psst, Wikipedia knows all.

http://en.wikipedia.org/wiki/Caret

:-)

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Quote:
Original post by Sneftel
Quote:
 Original post by SteadtlerI see the symbol here, maybe its your language set.
Yeh, now I see it on one of my computers but not the other.
Quote:
 Anyway, the *only* similar math symbol to both those characters is still the conjunction symbol.

Not true. In articles written in the days before TeX, and even these days in text-based circumstances, it's quite common to see ^ used for exponentiation. I've got some old Blinn papers in my filing cabinet at work that I'm almost certain use ^ in that way. It may be something which is specific to computer science literature.

Im not saying nobody does it, but its not proper nor widely accepted, and no math professor would use it on a blackboard. Plus, now that great tools exist, it should not be encouraged. Must have been a pain, doing science research in the days before Tex and the net.

Funnily enough, I had to revise one of my own articles because I had mistakenly used * for multiplication instead of the dot in one particular equation. The reviewers couldnt see why I was convoluting...

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Quote:
 Original post by SteadtlerIm not saying nobody does it, but its not proper nor widely accepted, and no math professor would use it on a blackboard.

Of course they wouldn't. They don't have to. The caret is used for exponentiation where superscripts aren't feasible. It's certainly widely accepted (see pretty much any Usenet FAQ involving math, for instance). As for "proper", I have no idea whether the Queen Mother considers it acceptable.

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Quote:
Original post by Sneftel
Quote:
 Original post by SteadtlerIm not saying nobody does it, but its not proper nor widely accepted, and no math professor would use it on a blackboard.

Of course they wouldn't. They don't have to. The caret is used for exponentiation where superscripts aren't feasible.

And thats what makes it unproper, and it should always be a priori and clearly defined when used as such, because the correct usage of ^ is for the conjunction, and using it for anything else only leads to confusion (as seen here).

tiegudanxin, I dont know what you are reading, but if it is for a mathematics class, then ^ means a logical "and". If its ALGOL then better read the language's semantic grammar...

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Quote:
 Original post by SteadtlerAnd thats what makes it unproper, and it should always be a priori and clearly defined when used as such, because the correct usage of ^ is for the conjunction, and using it for anything else only leads to confusion (as seen here).

You're using circular reasoning here. Do you have any evidence that more people mistake a caret-as-conjunction for a caret-as-exponentiation than the other way around? Honestly, I doubt many people would be confused by either.

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