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Logic and Proofs Videos 13 videos

Conditional Statements
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If you already know what a conditional statement is, then you're smarter than you look. And boy do you look smart.

Logical Reasoning (Problem)
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Indirect Proofs
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Indirect proofs (or proofs by contradiction) prove their conclusion by showing that the opposite cannot be true. You can use this in math and in ar...

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Formal Proofs 1858 Views


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Description:

Formal proofs present the oh-so-mathematical evidence in two columns: one for the statement they are claiming is true, and the other for the reasoning behind them.

Language:
English Language

Transcript

00:04

Formal Proofs, a la Shmoop.

00:09

Dear Sir or Madam, you are cordially invited to attend the Formal Proof,

00:15

a black tie event exclusively for geometers of the highest esteem.

00:20

Upon arrival, please form two columns and show this invitation at the door for admittance.

00:26

A-list members from all circles of the geometric world will be in attendance.

00:30

So please wear your best surface area, and enjoy live music,

00:35

complimentary cheesecake, and a night to remember.

00:38

Proofs are all about showing evidence for why something is true,

00:42

kind of like the detectives on your favorite crime show.

00:45

Formal proofs take this a step further.

00:48

They present the evidence in two columns:

00:51

one for the statement they're claiming is true

00:54

and the other for the reasoning behind them.

00:57

Usually these reasons take the form of definitions, theorems, postulates, or given information.

01:04

They lead us step-by-step from the hypothesis to the conclusion, like fancy tour guides.

01:11

So if A equals B and B equals C, can we prove that A equals C using a formal proof?

01:20

Well, let's give it a shot.

01:21

First, we'll make two columns: tone for statements, one for reasons.

01:24

We'll start with what we know.

01:26

We can say that A equals B, because that's given to us.

01:30

Same goes for B equalling C - given.

01:34

We want to prove that A equals C,

01:37

so we can use the transitive property of equality. That's all it takes.

01:43

We've proved what we wanted to prove using a formal proof.

01:46

Once you learn more definitions and theorems,

01:48

you'll be able to write longer, more complicated proofs. Don't look too excited.

01:52

If we can write formal proofs, we're certainly geometers of the highest esteem.

01:56

So let's head to that ball and have ourselves a big old hunk of cheesecakeā€¦

02:00

or five.

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