Proof by Contradiction: log₂5 is irrational

[ReinzyColle]

I was today years old when I made the connection that rational numbers are called rational because they are the RATIO of two integers.

[maarten]

2:36 Proof also that the clock on the wall is out of power.

[mxlexrd]

Once you reach 2^a = 5^b, you can also observe that this violates the uniqueness of prime factorisation.

[menachemsalomon]

I learned this (high school symbolic logic) as the laws _modus tollens_ and _modus ponens._ That is, given any conditional known to be true, you can prove the conclusion is true by showing that the antecedent is true. Conversely, you can prove the antecedent is false by showing the conclusion to be false. (That iss more accurately the contrapositive rather than the converse.)

[k.]

fuck sake Australia's so lucky they get to be in person with this guy.

[kailenmissen]

Thanks so much! These vids are helping me get through spesh units 1 and 2 and convincing me that I can continue with it in year 12. Very well explained and I understand it all

[epimaths]

lesson on logarithms, we can use small calculator to calculate.

[haneen]

You are an amazing teacher, thank you for sharing your knowledge and helping many students around the world appreciate the beauty of maths.

[sarahajbr]

i understood this way faster than i thought i would've 😭

[leftytaber]

On the board it says: " If P => Q is true then P => not Q if false." This is incorrect.. If P is a false statement then both are true. For example: "If 2 > 5 then 3=6" is a true statement.... but "if 2>5 then 3 is not equal to 6" is also true.

[mshajarrazip]

Watching this video made me interested in learning proofs.

but this wouldn't work for log base 3 5 which is irrational but at the same time we end up with 5^b=3^a where both are odd.

[reubenmanzo]

2:44 Looks like that clock doesn't work.

[dennis___]

One question: why did we establish a, b ∈ Z⁺ instead of a, b ∈ Q⁺ ?

[ahlamouldkhesal]

Brilliant but ...WE WANT MOOOORE!!!😊😊😊

[yoyozou]

Seemingly we've got a typical math class full of Asians :)

[ashwinparthiban]

a & b cannot be common factors too...

[adele]

What if a and b are both negative, x can still be positive

[himanshibhatiaa]

What happens if we want to involve two even or two odd numbers..like how can we prove for log 7 with base 3 ??

[bustin]

this is much easier than all of math 8