ok I have some problems that I need help with:

if a^2 is even, then prove that a is even too

if a^2 is uneven, then prove that a is uneven too

And another problem:

prove that:

rational + irrational number = irrational number

PLS HELP ME!!! (Doh)

- Sep 14th 2008, 09:00 AMantrewryAbout even and uneven numbers and about rational and irrational numbers
ok I have some problems that I need help with:

if a^2 is even, then prove that a is even too

if a^2 is uneven, then prove that a is uneven too

And another problem:

prove that:

rational + irrational number = irrational number

PLS HELP ME!!! (Doh) - Sep 14th 2008, 09:09 AMJhevon
use the contrapostive

it suffices to show if $\displaystyle a$ is not even, then $\displaystyle a^2$ is not even.

so assume $\displaystyle a$ is not even, so that $\displaystyle a = 2n + 1$ for some integer n, then .....

Quote:

if a^2 is uneven, then prove that a is uneven too

by the way, "odd" means "uneven" and it sounds nicer.

Quote:

And another problem:

prove that:

rational + irrational number = irrational number

PLS HELP ME!!! (Doh)

- Sep 14th 2008, 09:35 AMreagan3nc
Proof:

Let x be an even interger. Then by definition of an even number we can write:

x=2m

where m is an interger.

Therefore x^2= (2m)^2

=4m^2

=2(m^2)

Let P =2m^2. Since the product of integers is an interger, p is an itnerger. Thus x^2 =2p and x^2 is an even integer. - Sep 14th 2008, 09:40 AMMooQuote:

And another problem:

prove that:

rational + irrational number = irrational number

PLS HELP ME!!!

Quote:

Let $\displaystyle \frac ab$ be a rational number and c be an irrational number. what can you say about their sum?

Now, is it logical to say : $\displaystyle \underbrace{c}_{\text{irrational}}=\frac de-\frac ab=\frac{bd-ae}{be}$ ?

:D - Sep 14th 2008, 09:56 AMJhevon
- Sep 15th 2008, 08:34 AMantrewryOK not exactly
- Sep 15th 2008, 08:38 AMantrewry
- Sep 15th 2008, 08:43 AMantrewryThank you
- Sep 15th 2008, 04:33 PMJhevon