Tag Archives: surjection

Ways to prove a bijection

Posted on March 17, 2020 by Brent

You have a function and want to prove it is a bijection. What can you do? By the book A bijection is defined as a function which is both one-to-one and onto. So prove that is one-to-one, and prove that … Continue reading →

Posted in logic, proof | Tagged , , , , , , , , | 7 Comments

One-sided inverses, surjections, and injections

Posted on March 14, 2020 by Brent

Several commenters correctly answered the question from my previous post: if we have a function and such that for every , then is not necessarily invertible. Here are a few counterexamples: Commenter Buddha Buck came up with probably the simplest … Continue reading →

Posted in logic | Tagged , , , , , , | 1 Comment