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# Let’s Go Both Ways—If-and-Only-If Proofs

## Lecture no. 8 from the course: Prove It: The Art of Mathematical Argument

Taught by Professor Bruce H. Edwards | 31 min | Categories: The Great Courses Plus Online Mathematics Courses

Start with the simple case of an isosceles triangle, defined as having two equal sides or two equal angles. Discover that equal sides and equal angles apply to all isosceles triangles and are an example of an “if-and-only-if” theorem, which occurs throughout mathematics.

## 24 Lectures

1

What Are Proofs, and How Do I Do Them?

0 of 31 min

2

The Root of Proof—A Brief Look at Geometry

0 of 30 min

3

The Building Blocks—Introduction to Logic

0 of 30 min

4

More Blocks—Negations and Implications

0 of 30 min

5

Existence and Uniqueness—Quantifiers

0 of 30 min

6

The Simplest Road—Direct Proofs

0 of 30 min

7

Let’s Go Backward—Proofs by Contradiction

0 of 30 min

8

Let’s Go Both Ways—If-and-Only-If Proofs

0 of 31 min

9

The Language of Mathematics—Set Theory

0 of 30 min

10

Bigger and Bigger Sets—Infinite Sets

0 of 32 min

11

Mathematical Induction

0 of 30 min

12

Deeper and Deeper—More Induction

0 of 31 min

13

Strong Induction and the Fibonacci Numbers

0 of 30 min

14

I Exist Therefore I Am—Existence Proofs

0 of 31 min

15

I Am One of a Kind—Uniqueness Proofs

0 of 30 min

16

Let Me Count the Ways—Enumeration Proofs

0 of 31 min

17

Not True! Counterexamples and Paradoxes

0 of 29 min

18

When 1 = 2—False Proofs

0 of 31 min

19

A Picture Says It All—Visual Proofs

0 of 31 min

20

The Queen of Mathematics—Number Theory

0 of 28 min

21

Primal Studies—More Number Theory

0 of 31 min

22

Fun with Triangular and Square Numbers

0 of 30 min

23

Perfect Numbers and Mersenne Primes

0 of 30 min

24

Let’s Wrap It Up—The Number e

0 of 31 min

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