Infinity in math

[Ryan$]

Hi guys !
the teacher in the video said that the parallel of two lines will not be overlapped/cross each other just only on infinity ... what does that mean? if they're parallel then must stay parallel so how they in infinity cross each other? really weird ! may please anyone elaborate it to me?!
it's like if they are in parallel then how they will meet in infinity?! in infinity they must be also in parallel .

 

[topsquark]

To start with "infinity" is not a number. What Euclid was doing was creating an axiom (or postulate? I keep mixing those terms up) that is useful. I don't believe that he had the Mathematical "machinery" to discuss the concept of infinity in a structured way.

In fact, this axiom (or whatever) is useful in the extreme because if we assume that it isn't true then we get intersecting parallel lines, such as on the surface of the Earth. From this comes the fruitful Mathematics of non-Euclidean geometries.

-Dan

 

[Dr.Peterson]

the teacher in the video said that the parallel of two lines will not be overlapped/cross each other just only on infinity ... what does that mean? if they're parallel then must stay parallel so how they in infinity cross each other? really weird ! may please anyone elaborate it to me?!
it's like if they are in parallel then how they will meet in infinity?! in infinity they must be also in parallel .

Give us a link to the video, so we can know what we are commenting on!

Here are a couple pages about concepts that may be what he was referring to:

• https://www.math.toronto.edu/mathnet/questionCorner/infinity.html
• http://mathforum.org/library/drmath/view/52826.html
• https://www.cut-the-knot.org/WhatIs/Infinity/Projective.shtml

If he was talking about Euclidean geometry, on the other hand, he is wrong.