Proof by Contradiction (1 of 2: How does it work?)

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Dude, I am a 56 year old Ph.D. (Chemistry, from Purdue University) - I have always only learned the math I needed to "get by" in science. I have spent the last 5 hours watching you. You are amazing. I wish I had paid more attention in various math classes. Thank you! I cannot imagine why anyone would have a problem with any math with the internet available - especially with instruction by people like you. Thank you again!

buckdude

Never try to argue with a number that is not a ratio, they're irrational.

vinceperry

If you pay some attention to the rest of the classroom, you'll notice someone have drawn some kind of a special part of human body...

andreiavalentimvalentim

Proof by contradiction consists only of showing that set elements must belong to two sets that are mutually exclusive.

vinceperry

To prove "If P then Q" we assume "P is true and Q is false" not just "Q is false"

leftytaber

6:20 "we can demonstrate easily that given parallel lines, then alternate angles are equal." Exactly how do you demonstrate this easily? Isn't that an axiom?? Mathematicians have tried for 2000 years, in vain, to prove this
The converse "if alternate interior angles are equal, then the lines are parallel" is a theorem.

maxpercer

Godel's theorems are also proved. Maths would be nowhere without 'By Definition' statements . By definition statements don't need to be proved because they can't be proved. Don't mistake examples or justifications as 'proof'.

petermcgrandle

The models are the same, but the circles are bigger.

neverrip

Me, a Masters Computer science studenting watching him.

mohit

I understand that to present sophisticated ideas while teaching euclidean geometry is a terrible idea .
But a teacher must be careful NOT TO MISLEAD the student into to thinking that euclidean geometry is iron cld, always true
A proof in euclidean geometry is SEMI - iron clad!
IF an ONLY IF the axioms of euclidean are accepted as true... then YES indeed euclidean theorems are true.
But only I F-f-f-f euclidean axioms are true. Are they true?
BUT
(1) Euclidean geometry applied to outer space is a problem.
Einstein has shown that the shortest line between two points is NOT straight but curved due to space-time,
(2) Riemann geometry discards euclidean axiom 5 : that there are such a thing as parallel lines . Instead Riemann a geometry assumes the OPPOSITE of the axiom 5, . In Riemann geometry lines intersect at infinity

martinmartinmartin

Proof by contradiction was always my favorite!

andsykes

We know that a square has 360 degrees... An a triangle is basically 1/2 of a square. So that means triangles always has 180 degrees...

Marcus-hbdz

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