Math and Reality

[ydoaPs]

Math is fun because u can do things that you can't do in reality.

 

ex.1) Assymtotes

how in reality can one object approach another forever without the two objects meeting?

 

ex.2) Negative Distance

how can point A be closer to point B than point B is to itself?

[Sayonara]

ex.2) Negative Distance

how can point A be closer to point B than point B is to itself?

Tha one could work if you were able to generate a wormhole. But under those conditions I guess it wouldn't count as something that is "not in reality".

[bloodhound]

ex.2) Negative Distance

how can point A be closer to point B than point B is to itself?

 

dont know what u mean by negative distance.

 

From metric spaces: the distance function between objects from a set should satisfy these three axioms. if u have a metric space (d' date='A)

1)[math']d(a,b) \ge 0[/math]for all a,b belonging to A, and [math]d(a,b)=0[/math] if an only if a=b

2)[math]d(a,b)=d(b,a)[/math]

3)[math]d(a,c) \le d(a,b)+d(b,c)[/math] better known as the triangle inequality.

 

so by definition distance cannot be negative

[Tesseract]

Tha one could work if you were able to generate a wormhole. But under those conditions I guess it wouldn't count as something that is "not in reality".

 

I dont think that would be a wormhole.A wormhole would make point A as close as point B as point B is to itself, not closer.

[Sayonara]

I dont think that would be a wormhole.A wormhole would make point A as close as point B as point B is to itself, not closer.

You're assuming that the mouths of the wormhole are points A and B.

 

I am not.

[J'Dona]

ex.1) Assymtotes

how in reality can one object approach another forever without the two objects meeting?

Not only that, but when an object approached from the other side, the two objects would become increasingly different in values as they came closer together. (if you can apply values to objects...)

 

However, in terms of reality, there is one major case of this: mass as v ---> c. Or if you meant real objects, then watch as you drop something into a black hole, and it slows down until a point where it appears not to be moving, just on the event horizon (and then the photons run out and it disappears or something). It really has been wasted by the black hole, but it appears not to have been. Unless I'm mistaking the situation; I saw that on TV so there's a high chance it's wrong.

[ydoaPs]

wouldn't the two values become more similer? y would they be different?

[J'Dona]

Well, if you take the graph of something basic like , then as the x value approaches zero from the positive side the y value increases quickly, and when the x value approaches from the negative side the y value decreases quickly. So the y values are becoming more and more different as the two x values become closer.

[JaKiri]

ex.1) Assymtotes

how in reality can one object approach another forever without the two objects meeting?

 

Aside from the speed of light example already mentioned' date=' in terms of getting 'smaller', you can't, because of the limits of quantum reality. However, that's a problem with reality, rather than mathematics.

 

ex.2) Negative Distance

how can point A be closer to point B than point B is to itself?

 

You can't get negative 'distance' in this sense. 'Distance' is a scalar value, and thus is the modulus of displacement. Can you show me how a modulus of a value can be negative? You can get negative displacement, but that's a vector, and a negative value means it's the opposite direction

[JaKiri]

Well, if you take the graph of something basic like http://www.blike.com/tex/lateximg/pictures/54f0d4ac6307a2dfae5c80d83a39391d.gif[/img'], then as the x value approaches zero from the positive side the y value increases quickly, and when the x value approaches from the negative side the y value decreases quickly. So the y values are becoming more and more different as the two x values become closer.

 

This isn't necessarily true, you know. Try drawing the graph of 1/|x|.

[J'Dona]

Why does x always have to be positive?

[JaKiri]

Why does x always have to be positive?

 

What?

 

You also worded it extremely badly.

[J'Dona]

Erm... I think I forgot about cases where the y value tends to + or - infinity in the same way on both sides of the asymptote, like y = 1/|x| or y = 1/x². I was only thinking of cases like y = 1/x, where the y values tend to infinity in both the poitive and negative directions. That's why I wondered why x always had to be positive, because I was wasn't considering all cases, sorry about that. :/