Why exactly can't you divide by zero?

Added: 2026-06-03

[00:00:00]Why can't you divide by zero? It quietly breaks all of math. Let's see exactly why. Division is just multiplication backwards. 10 / 2 is 5 because 5 * 2 is 10. So, if 1 / 0 were some number X, then X * 0 would have to equal 1.

[00:00:19]But anything * 0 is 0, never 1.

[00:00:22]Impossible. Okay. But why do people guess the answer is infinity?

[00:00:27]Take a 1 kg chocolate bar. Break it into 500 g pieces. You get two. Into 100 g pieces, 10. 10 g pieces, 100.

[00:00:39]1 g pieces, 1,000.

[00:00:42]The smaller the piece, the more pieces you get. Push it to a thousandth of a gram, a million pieces. But here's the trap.

[00:00:50]How many 0 g pieces fit in the bar? You could keep taking nothing forever.

[00:00:55]Infinity.

[00:00:56]But then a 2 kg bar also gives infinity.

[00:00:59]So, 1 kg would equal 2 kg. That's absurd. The answer simply can't exist.

[00:01:05]Still unconvinced?

[00:01:07]Look at the graph of 1 over X. Coming in from the right, it shoots up to plus infinity. From the left, it dives to minus infinity.

[00:01:16]At zero, the two sides disagree completely. The answer can't be [music] plus infinity and minus infinity at once.

[00:01:24]So, math doesn't pick.

[00:01:26]It calls it strictly undefined.

[00:01:29]Want to see how limits make sense of all this?

[00:01:32]Watch the next one.