Question

All paths in R^2 are homotopic.

Answer 1

Proof by music video: https://www.youtube.com/watch?v=GF0cFOeyAJY

Answer 2

:)

Answer 3

well, the fact the fundamental group of \(\mathbb{R}^2\) is trivial is evidence of this -- there are no singularities to get in the way

Answer 4

Q.E.D.

Answer 5

boring real numbers as usual

Answer 6

true dat

Answer 7

there are some fun topologies you can get if you take away stuff.

Answer 8

lolol

Answer 9

https://www.youtube.com/watch?v=BipvGD-LCjU

Answer 10

:P

Answer 11

https://www.youtube.com/watch?v=SyD4p8_y8Kw

Answer 12

I hate to say it, but I never thought I'd be agreeing with Hitler