proof by contradiction

[analog swift]

this is the hardest pure topic imo

[simple cedar]

Assume n^2 is a multiple of 3 and n is not a multiple of 3
n = 3k+1,3k+2
n^2 can’t be a multiple of 3

So a contradiction has occurred, n^2 must be a multiple of 3

You could also have an argument about the prime factorisation

[limber pond]

not a multiple of 3 innit

[simple cedar]

All integers are of the form 3k,3k+1,3k+2

No

Cus you’ve missed out 3k+2

[limber pond]

well ur supposed to

[simple cedar]

Who the heck is that

[limber pond]

a level maths youtube guy

[simple cedar]

He probably did 3k-1,3k,3k+1

[analog swift]

zeeshan zamurred

[simple cedar]

Why are you watching people do a level maths

Just do it yourself

[limber pond]

fr

[simple cedar]

mik mik

It’s been like

2 years

[analog swift]

just derive it fr

[simple cedar]

Not cool

What would Clarence say

🤔 I think he’s missing a case

He would not 😔

@david

[analog swift]

if you can disprove it for only 3k+1 then isnt that sufficient

if it aint true for one case the statement isnt true at all

i could be yapping

[limber pond]

u would have to show it for 3k+2 too

[analog swift]

thats just what i think

looks like that question is from the textbook

check the solution bank if you can

[limber pond]

i think u would lose 1/3 for not checking 3k+2

[analog swift]

idk this topic is shit anyway

[limber pond]

ye its long

[analog swift]

better not be a 5 mark question on this in the exam

[limber pond]

i like when its just proving something is irrational

[analog swift]

induction 😍

me too

a2 integration is one of my easiest tho

[limber pond]

i havent done A2 integration yet people always say its the hardest topic

[analog swift]

its hard at first but then its beautiful

love a good old integral

[limber pond]

theres a lot of rules tho

compared to differentiation

[analog swift]

theres only about 3 no?

[limber pond]

is there?

[analog swift]

reverse chain, u sub and by parts

i cant think of anything else

[limber pond]

whys the chapter so long in the textbook tho

[analog swift]

theres other things like trapezium rule and something to do with differential equations i think

idk but once you get the hang of it it feels like only a few bits

[glacial jolt]

integration is harder than differentiation as theres multiple ways to integrate whereas differentiation its literally same thing every time

[gloomy axle]

We need to consider all values that aren’t a multiple of 3. Let’s say we let n=3k+2 and n^2 did actually lead to a multiple of 3 then do we assume the statement is actually true? If there is more than one case you’d need to include it to get all the marks

Cos otherwise it could be sometimes true