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Trifox
Account closed
Registered: Mar 2006
Posts: 108 |
calculating of square roots ?
hi all, for my newest project i am in urgent need to calculate the length of a 2d vector, reminding pythagorian math i remember that i have to calculate the roots of a fixed point (8bits.8bits) number, how can that be mastered in a convenient way ?!?!?!
thx
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_V_
Account closed
Registered: Jan 2002
Posts: 124 |
Graham: (pong)
>You still used equivalence and not infinity. You didn't
>use the series to calculate 2 but another formula.
I *did* use infinity because if I hadn't used the fact that the series has an infinite amount of terms, then I wouldn't have obtained the equivalence and hence the result. You can't see it due to the power of notation, but it's there.
>This is also the reason why there is an arrow towards
>infinity and not some equal-to-infinity stuff.
Uh, no, the arrow has nothing to do with the existence of an element. Because then I could also argue that 4 doesn't exist because I can write stuff like lim (n->4) 1/n. "Look, there's an arrow pointing at 4, thus 4 doesn't exist."
>The series cannot be infinite, infinity does not exist.
Okay. That is your viewpoint as a finitist. I have mine as an "infinitist". Now if you want to make me a believer, then prove formally that the element "infinity" doesn't exist. And don't do it just for me, because if you can really show this, then you will change the face of mathematics forever. Things like measure theory (which lead to integrals), Hilbert space (and thus quantum mechanics), projective geometry, statistics, fractals and extended number spaces will become entirely obsolete. |
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Copyfault
Registered: Dec 2001
Posts: 478 |
It's funny to read these ping-pong-posts from "the finitist" Graham and "the infinitist" _V_.
I somehow have the feeling that "math" has a different meaning for you two. While Graham seems to argue like an "applied scientist", _V_ seems to be the "pure mathmatician". What were you two guys doing irl ;) ?
In applied science, infinity is rather a concept than some "serious element" of whatever set. A term like
lim_{n -> +inf} f(n) = g
more or less means "ok, the bigger n is chosen, the smaller the difference between my calculations and the desired value g will be". At least this is what I was told during all my physics_stuff at the university, and, this is absolutely alright irl! And it will stay that way as long as no "infinitesimal precise" measurements can be done, which is a real problem if we take quantum mechanics for granted!
In "pure math", things turn out to be slightly different;) There is no prob in defining an element called "infinity" if the definition is coherent with the setting in which we're willing to define it! For mathmaticians, such socalled "welldefined" objects exist. There are even examples for proofs that show existance of some objects without being constructive! For me, I have to admit, is this the beautiful part of math;))
Looking forward to seeing more ping-pongs from you - damn it I'll for sure won't make it to X this year:/
CF |
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Graham
Account closed
Registered: Dec 2002
Posts: 990 |
Computer science is kinda the "extension of math" and it also has to deal with infinity. A lot of problems can be proven unsolvable because of infinity.
Anyway my point was: You do not actually use infinity to calculate something because you can't. |
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enthusi
Registered: May 2004
Posts: 677 |
V:
inf (again/still) is no value.
Whenever you have an equation with inf in it, its bogus.
You can 'imagine' (not compute) what the limes of something towards inf would be and then use that expression *instead* and get a result (as you did above).
And especially mathematicians (those I dealt with for quite some time :) are very very careful about limes-stuff.
Actually they hate it :)
It is merely a concept - a necessary one of course to connect things we can describe and things that exist.
A circle can be described with some lim/inf-stuff but you can not compute it that way. Just as you cant compute pi - even if you have an unlimited amount of time :)
All the integral-stuff you mentioned is applied to concepts, not to calculations.
You do not calc inf no of steps. Instead you show that you get from a to b via the concept of lim/inf and THEN you calc b, since it now is freed of inf.
As graham explained, you didnt compute the result using inf, but converted/transformed it instead.
I too claim (but unfortunately Im very much not to first to do so) that infinity does not exist. Not in the world perceptible to us.
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Graham
Account closed
Registered: Dec 2002
Posts: 990 |
Also please note that once you do not have an equivalence of something infinite to something finite, you cannot calculate it. There is a huge set of unsolvable/uncalculateable problems due to that. |
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_V_
Account closed
Registered: Jan 2002
Posts: 124 |
Copyfault is right in pointing out that I have been talking about the element "Infinity" as viewed in pure mathematics. Mathematicians like to extend the real number line with the elements +/-Infinity, as they can then prove it to be isomorphic with the closed interval [0,1] and make the set compact, which is a very attractive property in topology. Apparently, mathematicians are idiots to do this because infinity doesn't exist.
Graham:
>Anyway my point was: You do not actually use infinity to >calculate something because you can't.
Enthusi:
>As graham explained, you didnt compute the result using
>inf, but converted/transformed it instead.
Except that I *did*. I _used Inf_ to _convert_ the expression and obtain the exact result.
1/+Inf = 0
Whoops, I just used Infinity again to calculate something :). And I didn't even write lim anymore. All nicely done in the extended real number line, of course.
>inf (again/still) is no value.
That's why I said that +Inf is a numberless number. It certainly isn't a "real number" like pi, but it still is the element used to extend the reals.
>Whenever you have an equation with inf in it, its bogus.
Quite bogus to say, considering that the majority of physical and mathematical theories are crawling with infinities of all kinds. Hence those theories must be bogus, too?
>You can 'imagine' (not compute) what the limes of
>something towards inf would be and then use that
>expression *instead* and get a result (as you did above).
In my computation, I'm not going towards infinity. I'm already there because I'm dealing with the infinite object, the infinite series itself. By the way, wouldn't you say that imagination/reasoning is a form of computation?
>Just as you cant compute pi - even if you have an
>unlimited amount of time :)
You will have determined pi, or any irrational number, exactly at infinity units of time :).
>And especially mathematicians (those I dealt with for >quite some time :) are very very careful about limes-stuff.
Of course, but from ym experience, I'm quite sure that their concern is mainly focused on the convergence behaviour of the object under scrutiny, not the actual limit per se.
>I too claim (but unfortunately Im very much not to first
>to do so) that infinity does not exist. Not in the world
>perceptible to us.
Whether or not infinity exists in the physical world must still be proven. I'm definitely not going into it. Conceptually, though, it's certainly there.
>Also please note that once you do not have an equivalence
>of something infinite to something finite, you cannot
>calculate it. There is a huge set of
>unsolvable/uncalculateable problems due to that.
That's a statement I'm not going too deeply into either, because this is part of the realm of logical theories and undecidable sentences, which still is a vast, uncharted territory. Suffice to say, I believe that any undecidable problem in one theory can be decidable in another theory. Hence - given that you look hard enough - you can prove/solve/calculate anything, but only within your theory of choice. I believe that everything is relative - even the fabric of mathematics itself.
I'll leave you with a question to think about: does the Sierpinski triangle exist? |
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chatGPZ
Registered: Dec 2001
Posts: 11386 |
Quote:I'll leave you with a question to think about: does the Sierpinski triangle exist?
that one is quite an interisting problem :=) go a step further and create a pyramid using the same recursion... and you'll get an object with infinite surface but zero volume... o_O |
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JackAsser
Registered: Jun 2002
Posts: 2014 |
1/+Inf = 0 is bogus since then 0*(+Inf) = 1 which it clearly isn't... :D
My point is that dealing with +-Inf without the concept of limes is delicate and can easily lead to obscure results as the above. |
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Graham
Account closed
Registered: Dec 2002
Posts: 990 |
Oh well... Infinity is just a concept and no number. It is not imaginable, only a few rules of how something infinite would behave is imaginable. But applying these rules is not equal to applying infinity.
Oh, and nopes, the Sierpinski Triangle does not exist. Only the rule of how you could build one IF infinity existed. But ofcourse: Infinity does not exist. |
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chatGPZ
Registered: Dec 2001
Posts: 11386 |
Quote:Oh, and nopes, the Sierpinski Triangle does not exist. Only the rule of how you could build one IF infinity existed. But ofcourse: Infinity does not exist.
and the sierpinsky "pyramid" demonstrates it quite well... an object with zero volume does not exist :=) |
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