Proof: Cancellation Law for Cartesian Products | Set Theory скачать в хорошем качестве

Proof: Cancellation Law for Cartesian Products | Set Theory

We prove the cancellation law for cartesian products. Suppose A, B, and C are sets with C nonempty. Then AxC=BxC. This is a straightforward set equality proof, we first have to consider the case where A is empty. Then, we'll suppose it is nonempty, and show A is a subset of B. It is the same logic as assuming B is nonempty and showing B is a subset of A. #SetTheory Recall the cartesian product AxC is the set of all ordered pairs (a,c) where a is in A and c is in C. Cartesian Products:    • What is the Cartesian Product of Sets? | S...   Cartesian Products with Empty Sets:    • Cartesian Products with Empty Sets | Set T...   ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Thanks to Robert Rennie, Barbara Sharrock, and Rolf Waefler for their generous support on Patreon! Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Music Channel:    / @emery3050