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what is meaning of ^ symbol in math?


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#1 tiegudanxin   Members   -  Reputation: 122

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Posted 03 June 2007 - 11:54 AM

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

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#2 nilkn   Members   -  Reputation: 960

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Posted 03 June 2007 - 11:56 AM

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

#3 rip-off   Moderators   -  Reputation: 7623

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Posted 03 June 2007 - 11:58 AM

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.

#4 Zipster   Crossbones+   -  Reputation: 545

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Posted 03 June 2007 - 12:54 PM

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

#5 tiegudanxin   Members   -  Reputation: 122

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Posted 03 June 2007 - 01:30 PM

Thank you.

#6 Steadtler   Members   -  Reputation: 220

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Posted 04 June 2007 - 11:51 AM

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.

#7 Sneftel   Senior Moderators   -  Reputation: 1776

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Posted 04 June 2007 - 12:52 PM

Quote:
Original post by Steadtler
The ^ 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.

#8 Roboguy   Members   -  Reputation: 794

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Posted 04 June 2007 - 01:03 PM

Quote:
Original post by Steadtler
Guys, 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 Steadtler
The ^ 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.

#9 Kimani   Members   -  Reputation: 104

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Posted 04 June 2007 - 01:05 PM

Quote:
Original post by Steadtler
Guys, 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.

#10 jpab   Members   -  Reputation: 881

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Posted 04 June 2007 - 01:09 PM

Quote:
Original post by Kimani
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.

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

#11 Steadtler   Members   -  Reputation: 220

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Posted 04 June 2007 - 01:25 PM

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]

#12 Steadtler   Members   -  Reputation: 220

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Posted 04 June 2007 - 01:31 PM

Quote:
Original post by Kimani
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.


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.


#13 instinKt   Members   -  Reputation: 148

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Posted 04 June 2007 - 01:43 PM

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

School rocks!


#14 Sneftel   Senior Moderators   -  Reputation: 1776

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Posted 04 June 2007 - 01:45 PM

Quote:
Original post by Steadtler
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.

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.

#15 Steadtler   Members   -  Reputation: 220

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Posted 04 June 2007 - 01:48 PM

Quote:
Original post by instinKt
A 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!

#16 Paradigm Shifter   Crossbones+   -  Reputation: 5094

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Posted 04 June 2007 - 02:34 PM

When I see ^ in maths, it's either

cross product (most texts use X though)

set intersection (normally bigger wigwam though)
"Most people think, great God will come from the sky, take away everything, and make everybody feel high" - Bob Marley

#17 Steadtler   Members   -  Reputation: 220

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Posted 04 June 2007 - 03:46 PM

Quote:
Original post by Sneftel
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.


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.

#18 Sneftel   Senior Moderators   -  Reputation: 1776

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Posted 04 June 2007 - 03:53 PM

Quote:
Original post by Steadtler
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.

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.

#19 Steadtler   Members   -  Reputation: 220

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Posted 04 June 2007 - 04:26 PM

Quote:
Original post by Sneftel
Quote:
Original post by Steadtler
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.

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.

#20 Sneftel   Senior Moderators   -  Reputation: 1776

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Posted 04 June 2007 - 05:08 PM

Quote:
Original post by Steadtler
I 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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