 One basic rule of mathematics is that multiplication is commutative. So 3 times 4 is the same as 4 times 3. It seems obvious, but I can't seem to get a rigid understanding of why it works. Just break it down. Just break it down. Here. I'm going to erase this. So commutative, because 3 of 4 is the same as 4 of 3, basically. Bring math. Wow. Cool. Cool. Math. So watch this. 4 times 3 is the same thing as 3 times 4. 4 times 3, you can interpret it as saying 4 things added together 3 times. That's what multiplication is. Multiplication is an extension of addition. So when you write this, you're saying 4 plus 4 plus 4. It's just a faster way of writing 4 plus 4 plus 4. That's what 4 times 3 is. 3 times 4 is really 3 plus 3 plus 3 plus 3. Now what's the proof of this? I don't know what the official proof of this is. But if you add these up, if you do the addition of it, this is equal to 12. And if you add these up, this is equal to 12, so 12 is equal to 12. And this is an official proof. This is just a visualization of how it works. As for the official proof, this is one of the axioms of mathematics, and I forget what the proof is. I've looked into it before. Four basic properties, cumulative, distributive, transmittive, and identity. Or I think they're called axioms. Yeah, the axioms of math. There's actually five axioms of mathematics. One of them is distributive, cumulative. Is that what this is? I don't know what the fifth one is. I think mathematics is based on five axioms. I can't remember what the fifth one is.