what is meaning of ^ symbol in math?

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44 comments, last by erissian 16 years, 10 months ago
Quote:Original post by instinKt
Quote:Original post by joanusdmentia
Quote:Original post by instinKt
A friend of mine was told there was no such thing as negative natural numbers.


Fixed.


Don't defend a lousy teacher who was too lazy to explain to the other kids what a negative number was!


Don't defend a smart-ass student who thinks he's cool by dropping 1 word and saying 'OMG MY TAECHER CANT DO MATH!'.....or at least I hope that's what happened [smile]
"Voilà! In view, a humble vaudevillian veteran, cast vicariously as both victim and villain by the vicissitudes of Fate. This visage, no mere veneer of vanity, is a vestige of the vox populi, now vacant, vanished. However, this valorous visitation of a bygone vexation stands vivified, and has vowed to vanquish these venal and virulent vermin vanguarding vice and vouchsafing the violently vicious and voracious violation of volition. The only verdict is vengeance; a vendetta held as a votive, not in vain, for the value and veracity of such shall one day vindicate the vigilant and the virtuous. Verily, this vichyssoise of verbiage veers most verbose, so let me simply add that it's my very good honor to meet you and you may call me V.".....V
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Quote:Original post by TheAdmiral
Quote:Original post by Steadtler
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.

That's pretty narrow-minded. There is no universal standard for mathematics, just convention. While you may prefer to have ^ default to logical conjunction, there is no denying that it is commonly used for a whole variety of other things, and hence it represents them. Hell, I've seen some horribly perverse notation in my days, but I've never claimed ant of it to be 'wrong'. Indeed, if the writer defines their own notation, that's their prerogative and nobody can refute their use of it.

The whole argument's pretty much moot anyway. I would hope it's very clear from the context what is meant.

Admiral


Exactly. For example, λ-calculus is math, but it's use of λ is completely different than it's use when analyzing waves in physics. All of programming is, in some sense, a form math, as well.

Like I said, it all depends on context.
Quote:Original post by joanusdmentia
Quote:Original post by instinKt
Quote:Original post by joanusdmentia
Quote:Original post by instinKt
A friend of mine was told there was no such thing as negative natural numbers.


Fixed.


Don't defend a lousy teacher who was too lazy to explain to the other kids what a negative number was!


Don't defend a smart-ass student who thinks he's cool by dropping 1 word and saying 'OMG MY TAECHER CANT DO MATH!'.....or at least I hope that's what happened [smile]


Nope, not what happened at all. I'm not saying she couldn't do math, just that she didn't want to explain to the other kids what a negative number was. Lazy teachers ftl.
Daerex is correct. If you have LaTeX, \wedge is the conjunction symbol. You'll notice it's taller and more acute than a caret. There's also \bigwedge, too, for "distributing" a conjunction over a list of terms (in the same way that sigma "distributes" addition over a list of numbers).
It is amusing that the lambda calculus would be mentioned in the same thread as the circumflex symbol (^). Since amusingly enough, the lambda notation is a direct descendent of the circumflex. The mutation from ^ to lambda is an interesting bit of trivia. I will tell the story if anyone is interested.
Quote:Original post by instinKt
Quote:Original post by joanusdmentia
Quote:Original post by instinKt
Quote:Original post by joanusdmentia
Quote:Original post by instinKt
A friend of mine was told there was no such thing as negative natural numbers.


Fixed.


Don't defend a lousy teacher who was too lazy to explain to the other kids what a negative number was!


Don't defend a smart-ass student who thinks he's cool by dropping 1 word and saying 'OMG MY TAECHER CANT DO MATH!'.....or at least I hope that's what happened [smile]


Nope, not what happened at all. I'm not saying she couldn't do math, just that she didn't want to explain to the other kids what a negative number was. Lazy teachers ftl.


Likely she was never taught the concept of number well enough to be able to accurately articulate an explanation or even understand for herself what it means for a number to be negative. Which is not surprising considering how the qualifier negative do nothing but confuse the situation, they might as well be Dark numbers or Bad numbers.

Do you know what a negative number is?
Quote:Original post by Daerax
It is amusing that the lambda calculus would be mentioned in the same thread as the circumflex symbol (^). Since amusingly enough, the lambda notation is a direct descendent of the circumflex. The mutation from ^ to lambda is an interesting bit of trivia. I will tell the story if anyone is interested.


I would be interested in hearing it. I've seen that notation used, but I never really knew why it was used.
Quote:Original post by Daerax
It is amusing that the lambda calculus would be mentioned in the same thread as the circumflex symbol (^). Since amusingly enough, the lambda notation is a direct descendent of the circumflex. The mutation from ^ to lambda is an interesting bit of trivia. I will tell the story if anyone is interested.

Go for it.
I have seen two histories, one which implies the mutation was controlled by Church the other which implies it was accidental.

Both agree that Church based his original lambda calculus notation on Russell and Whitehead's principia mathematica (Church's work in general drew much from it) which used
  ^f(x) to denote a function whose application would result in f(x). Church modified it too ^x.f(x) for succintness.
But the type setter, like this forum could not put the circumflex on top of the x so it became ^x.f(x), here is where the story diverges. Some say this was mistaken for Λ where it mutated to λ under another typesetter.

The other story, which is the one I prefer states that after finding out there was no typesetting which allowed the circumflex to be on top Church decided to move it to the left but use Λ (capital lambda) instead. He decided it looked too much like the conjunction symbol and so made it the lower case lambda. Hence λx.f(x).
Quote:Original post by Daerax
Quote:Original post by instinKt
Quote:Original post by joanusdmentia
Quote:Original post by instinKt
Quote:Original post by joanusdmentia
Quote:Original post by instinKt
A friend of mine was told there was no such thing as negative natural numbers.


Fixed.


Don't defend a lousy teacher who was too lazy to explain to the other kids what a negative number was!


Don't defend a smart-ass student who thinks he's cool by dropping 1 word and saying 'OMG MY TAECHER CANT DO MATH!'.....or at least I hope that's what happened [smile]


Nope, not what happened at all. I'm not saying she couldn't do math, just that she didn't want to explain to the other kids what a negative number was. Lazy teachers ftl.


Likely she was never taught the concept of number well enough to be able to accurately articulate an explanation or even understand for herself what it means for a number to be negative. Which is not surprising considering how the qualifier negative do nothing but confuse the situation, they might as well be Dark numbers or Bad numbers.

Do you know what a negative number is?


Same as a positive number just with a '-' in front! duh ;P
(Really just wanted to add another level of quoting, it looks pretty)

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