throwfermat

Here is a nice one I read sometime back.

Create a video of your friend walking 3 metres. Now play the video 4 times. Your friend walks 12 metres in the video. Play the video in reverse 4 times. Your friend walks 12 metres backwards in the video.

Create another video of your friend walking backwards 3 metres. Now play the video 4 times. Your friend walks 12 metres backwards in the video. Play the video in reverse 4 times. Your friend walks 12 metres forwards in the video.

There is a discussion in this post's comments section⁽¹⁾ that this works for fields and rings too.

I know there are precise definitions for fields and rings but can someone here give me some good examples of fields and rings? Being a non-mathematician, I find it easy to manipulate examples than manipulate definitions.

Are the set of integers a field? I guess not because the multiplicative inverse of 2 is not present in this set.

Is the set of integers a ring? I think, yes.

For prime p, is Z_p = {0, 1, ..., p - 1} a field? I think, yes.

Are there any non-numeric rings where product of negatives is positive?

⁽¹⁾ https://susam.in/blog/product-of-negatives/comments/