How many injective functions

So, how many injections are there? Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Asked 3 years, 7 months ago. Active 3 years, 7 months ago. Viewed 2k times. Recall the definition of a function. De Morgan's Laws 4. Mixed Quantifiers 5. Logic and Sets 6. Families of Sets 2 Proofs 1. Direct Proofs 2.

Divisibility 3. Existence proofs 4. Induction 5. Uniqueness Arguments 6. Indirect Proof 3 Number Theory 1. Congruence 2. The Euclidean Algorithm 4. The Fundamental Theorem of Arithmetic 6. The Chinese Remainder Theorem 8. The Euler Phi Function 9. The Phi Function—Continued Wilson's Theorem and Euler's Theorem Public Key Cryptography A function is a way of matching the members of a set "A" to a set "B":.

Surjective means that every "B" has at least one matching "A" maybe more than one. Think of it as a "perfect pairing" between the sets: every one has a partner and no one is left out. If every "A" goes to a unique "B", and every "B" has a matching "A" then we can go back and forwards without being led astray.

This is not a function because we have an A with many B. It fails the "Vertical Line Test" and so is not a function. But is still a valid relationship, so don't get angry with it.

A General Function.