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Negative numbers don't exist proof inside

#31 User is offline   David-kyo Icon

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Posted 21 September 2008 - 07:59 PM

Mostly tl;dr but I haven't see anyone object to the fact that Ffreak took the square root of a negative number in one of the steps. I'm no mathematician but from what I recall, that has about as much sense as dividing by zero.
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#32 User is offline   Ninja Duck Icon

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Posted 21 September 2008 - 09:07 PM

David: You may want to read up on complex numbers. The square root of negative one is an imaginary number.

Slade: If you were referring to the complex number system with that comment, imaginary numbers do have applications in engineering. Physics isn't my forte, but imaginary numbers are used to describe the motion of quantum particles, for example Schrodinger's equation.

Patch: So different rules apply in different frames, but I still don't see how that means math is subjective and postmodernist. You're right that math is only as true as the assumptions it's based on, but the axioms that much of math is based on are so obvious (at least when they're in human-readable terms) that you'd have to be ca-razy to deny them. And you can judge from the fact that we don't have wildly wrong conclusions that our assumptions must be okay. Or else Bertrand Russell would be the pope.

This post has been edited by Ninja Duck: 21 September 2008 - 09:12 PM

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#33 User is offline   FFreak3 Icon

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Posted 22 September 2008 - 03:39 AM

I never said that math is subjective or post-modernist.

I said that math is made up to be useful, (then if possible, made general and easy).
You can have two perfectly correct maths which conflict with each other in ways we don't understand, that are based on the same logic, just different assumptions.
. . . any of which, you'd have to be crazy to deny, it seems.

Assumptions can be not quite right, y'know. The easiest way is to have extra conditions, or be missing conditions, to have false postulates or to have ambiguous wording. It's always interesting to look up the history of the changing of assumptions from an area of math, particularly algebra since many mathematicians STILL argue that it shouldn't be part of real math. (but you'd be hard pressed to find someone who wants to get rid of it completely, since it's so damn handy).
Actually, even looking at Euclid's geometry you can see many changes.
To his highly debated 5th postulate: that any two lines, which, when they have line drawn between them, have interior angles on one side of that line equal to less than 180 degrees, will meet on that side, we have added quite a few conditions.
For one, they have to be in 2-dimensional space, (which was not stated, but implied).
They cannot be mapped on complex numbers, (but real numbers are okay).
They have to be continuous. (which was implied)
They are not unique, (which was implied by the rest of his postulates).
. . . and so on. It's actually quite the list.

Notice that no one actually disagreed with Euclid, they just thought he didn't include enough conditions to make it true. It is still possible to come up with additional conditions needed to make Euclid's postulate true . . . there is, in fact, a reward given out by an Italian University every year for people who create a new condition which was neither implied nor derivable from previous conditions for Euclid's 5th Postulate.
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