What does modulo mean? — The Ross Program

Often "modulo" means to compute the remainder after division, but as we dig deeper into number theory, we'll use "modulo" to mean more than just an arithmetic operation.

[mavaction]

Maybe a shortcut to visualizing modulo. To think in modulo 5 ... cut a circle into 5 pieces and wrap the counting numbers around the circle. Now the modulo 5 property is the same as the phase angle of the number. So 6 occurs at the same angle as 11 and 16 etc... all these numbers are 1/5th the way around the mod 5 circle.

[inclinacionmatematica]

Teacher: “Modulo is a word that didn’t exist in English! But we needed it”
Me, a non native English speaker: “Cycle?…”

[tsokiyzan]

mod 7 is a week, then the 1st, 8th, 15th, 22nd, and 29th are all "equal" (they are all mondays)

[gentlemandude]

I wish I were studying at OSU. I'd love to study mathematics with you. Thank you for these wonderful videos.

[ttttt_]

I'd think writing Z5 as Z/5Z would be more appropriate since as a quotient it exactly means what you want it to be thought of. Then you also wouldn't have to argue about not treating them a integers since they are sets. Are you going to further Explore this argument?

Anyways, it was still a nice video to watch ;)

[robertweston]

I kept waiting for a discussion about equivalence classes and how the elements of Z5 name them, but didn't hear the word 'equivalence' until the end. How come?
Also, I love the questions at the end. Too often we get caught up in the linearity of textbook chapters and forget to ask good, or any 'What if' questions.