deducing that e is irrational (1 Viewer)

[Affinity]

Re: 回复: Re: 回复: Re: deducing that e is irrational

nah it's not that i do'nt accept wiki's proof or antyhing as i don't know how to prove it myself.

but shaon0 is implying the proof is 'easy' when he hasn't been able to show his own proof which is devised by his own thought, and not wiki's.

In mathematics almost all notions and results are universally accepted by those who studied it.. the other side of this is that sometimes there aren't too many different ways to prove something..

The proof given above is probably the most elementary and is quite straightforward..

 

[Iruka]

I always knew that thing as Euclid's proof, rather than infinite descent. It is pretty much the same thing though. I suppose you could also do another proof where you invoke the Fundamental Theorem of Arithmetic (a.k.a. Prime Factorisation Theorem), but it would basically be the same as Euclid's proof.

 

[duy.le]

Re: 回复: Re: 回复: Re: deducing that e is irrational

i only know the proof by infinite descent which unfortunately is already claimed by wiki

even though thats on wiki its rather quite easy to understand and follow, ive seen it before but i just never knew the name of it, always thought it was just prove by contradiction (even though thats not a name).

though i would doubt that its in the hsc cause of its trivality and simplicity. however i do have notes on it though. lol. for some reason.

edit: i would say that the wiki proof is even easier to understand than lolokay's proof, though they are very similar. i just fail to understand it fully.

 

[shaon0]

Re: 回复: Re: deducing that e is irrational

Still waiting on a non-wiki proof by shaon0

oh sorry, i would have proved it but i'm currently having some weird internet problems.

but you just use sqrt(2)=p/q since every rational number excluding some freaks which aren't known as irrational or rational ie. Euler's number (approx. 0.577) and so on.
then u just square both sides; 2=p^2/q^2.
Thus, 2 q^2=p^2. since, the square of p is an even no. it ihas to satisfy two times whatever. THus, p is an even no. since p is two times another number.
p=2m where m is some no.
Let p=2m and sub this into the original equation.
then; 2=(2m)^2/q^2
2=4m^2/q^2
2q^2=4m^2
Thus, q^2=2m^2.
This means b^2 must be an even no.
THus, sqrt(2) isn't rational.

Tell me if theres any whole's in my proof i may have assumed something that i didn't have to

 

[shaon0]

Re: 回复: Re: 回复: Re: deducing that e is irrational

i only know the proof by infinite descent which unfortunately is already claimed by wiki

seriously, don't go on wikipedia for math, its way too complicated. Gives me a headache even looking at it.

 

[Js^-1]

Re: 回复: Re: 回复: Re: deducing that e is irrational

I conquer. Wiki isn't the best for easy to understand mathematical or science concepts.

 

[duy.le]

Re: 回复: Re: 回复: Re: deducing that e is irrational

I conquer. Wiki isn't the best for easy to understand mathematical or science concepts.

LOLOLOLOLO:rofl: sorry just a very funny mistake

 

[Js^-1]

Re: 回复: Re: 回复: Re: deducing that e is irrational

*concur

It was a joke from the Simpsons. Lenny (or Carl, I can never remember) has a word of the day calender. The word for the day is conquer, and when homer says something to which Lenny agrees, he says "I conquer" ('aye kon-ker'). It's very amusing, I suppose I should have explained it.