What is the Cartesian Product of Sets? | Set Theory

What is the Cartesian product of two sets? The Cartesian product can be generalized to more than two sets, but in this video we go over Cartesian products of two sets! Here is how it works. If you have two sets, A and B, then their Cartesian product, written A x B, is the set containing all ordered pairs (a, b) where a is in A and b is in B. For example, {1, 2, 3} x {x, y, z} = { (1, x), (1, y), (1, z), (2, x), (2, y), (2, z), (3, x), (3, y), (3, z) }. Notice that the cardinality of A x B is equal to the product of the cardinalities of A and B. That is, |A x B| = |A| * |B|. This is always true.

I hope you find this video helpful, and be sure to ask any questions down in the comments!

+WRATH OF MATH+

Follow Wrath of Math on...

[riittap]

You wrote AXB = BXA while explaining at the same time, that they are not equal. I was looking for the correction, but it never came. I hope people didn't find this confusing, at least noone has complaint about it. Great videos!

[jingyiwang]

Thank you for another clear explanation about the Cartesian Product of Sets. I have been a huge fan of the mathematical videos made by you for quite a long time. All of them are really helpful!

[ankita]

Great video. The best explanation among the 5 videos I watched, specially the bit at the end, where you explained the X and the Y axis. Nobody did that.

[chazy]

Oh my God, sir I wanted this video..Thankyou so much.🙏🏻🙏🏻

[moniquefaithboodram]

Thanks so much! Most helpful video on Cartesian products 🥳

[kelvinmusukuma]

this has been very helpful thankyou and i like the song that you play at the end of your videos how can i download it

[michmuch]

Thanks for the vid....I had a question. My math teacher told me that in sets, neither order nor repetition is of any relevance and that sets are equal if they have the same elements order and repetition not Doesn't that mean that Cartesian products are commutative?

[Nuhahossainy]

Is there an example from physics that shows Cartesian multiplication?

[jennyrosetrujello]

This is cool! I've been looking for this one. Thank you for sharing this to us, it really helps.