stupid proofs ----> e (1 Viewer)

[CM_Tutor]

An irrational number is a real number that cannot be written in the form p / q, where p and q are integers, q <> 0, and p and q have no common factors other than 1. You encounter irrational numbers all the time - sqrt(2) and pi, to name two.

A transcendental number is an irrational number that is not the solution of any finite polynomial with rational coefficients.

For example, an irrational like sqrt(2) is the solution of any number of finite polynoimials, like x² - 2 = 0, or
x⁴ + 4 = 4x².

For a transcendental number, like pi or e, no such polynomials exist.

 

[Grey Council]

o

cause I remember one of the solutions to Buchanan's question to "prove pi is irrational" was a one line answer:
Pi is transcendental.

i doubt full marks would have been awarded to that answer though.

thanks, btw. I tried searching for a dictionary definition, but it was SSOOO vague, its not funny.

 

[Xayma]

Yeah I think you are expected to prove that it is transcendental in the HSC unless it states it in the syllabus that it is transcendental.

 

[KeypadSDM]

Proving it's trancedental is a bitch tho.

 

[Grey Council]

lol, i doubt most people would have even HEARD of a transcendental number.

Out of curiosity, have you ever tried to do it Keypad? and hows Uni?

 

[McLake]

Originally posted by Grey Council
lol, i doubt most people would have even HEARD of a transcendental number.

Our 4U teacher taught us about it ...

 

[CM_Tutor]

Originally posted by turtle_2468
And, just in case anyone asks, you DON'T need to know taylor series for HSC
Although, it MIGHT be given to you... so freak out ppls! (really. Don't worry about it)

I just put up an example of this in the thread "complex no. problem"

 

[sammeh]

irrationality of pi was question 8 on '03 paper i think? anyways check that out its a similar proof as i remember...maybe...

once more i attribute my vaguess to recent glandular fever suffering. hmm maybe i should just add that to my sig ;p

 

[KeypadSDM]

Originally posted by Grey Council
Out of curiosity, have you ever tried to do it Keypad? and hows Uni?

Nope, bit I've tried to prove e^Pi is.

That one's an easy one

e^Pi = e^{(- iPi) * i}
=(-1)ⁱ
Of the form a^b where a, b algebraic, b irrational.

Thus e^Pi is trancedental.

Or something like that ...

 

[CM_Tutor]

Originally posted by KeypadSDM
Nope, bit I've tried to prove e^Pi is.

That one's an easy one

e^Pi = e^{(- iPi) * i}
=(-1)ⁱ
Of the form a^b where a, b algebraic, b irrational.

Thus e^Pi is trancedental.

Or something like that ...

Is i irrational? I thought irrationals had to be real.

 

[KeypadSDM]

So did I, but there's some crazy proof somewhere ...

I think...

I think it's in wolfram ... *checks*

 

[KeypadSDM]

http://mathworld.wolfram.com/GelfondsTheorem.html

There it is.

I believe wolfram...

 

[CM_Tutor]

Originally posted by CM_Tutor
Is i irrational? I thought irrationals had to be real.

Originally posted by KeypadSDM
So did I, but there's some crazy proof somewhere ...

I think...

I think it's in wolfram ... *checks* ...

http://mathworld.wolfram.com/GelfondsTheorem.html

There it is.

I believe wolfram...

Well, you learn something new every day. Thanks