I had a thought...

[Kitsadoodles]

1 is neither a prime or composite number, just because it is. there is really no reason for it, its just 1 and nothing else. every single math teacher i've had tells us that it just is. maybe the world will never know.......

[whiteninja]

"i" is used to denote an imaginary number, so Miri was right with that one.

0 is neither negative, nor positive, nor prime (0*1=0, but so does 0*2, and 0*3 and 0*...) and contrary to what all those math teachers tell you: a number divided by 0 is not undefined! It's infinity!!!! It is! because if division is the number of times you can subtract number "x" from number "y", then if "x" is 0, you can subtract that infinite times from "y"! You can't subtract it undefined times!!!!!! It's infinity I tell you!!!!!! Iiiiiinnnnnfffffffiiiiiiinnnnnnnniiiiiiiiittttttttttyyyyyyyyyy!!!!!!!!![/rant]

Prime numbers have only themselves and 1 as factors, and they are not negative.

1 is prime, but it is not counted as an odd number.

The only even number that is prime is 2.

3 is the first prime number that is also odd.

An even power of any number is positve, whereas an odd power of a positive number is positive and of a negative is negative. The 0th power is always one. So 0^0=1, as weird as that is.

The square roots of all negative numbers are imaginary, and so are the even powered roots, but the odd powered roots of negative numbers are negative numbers.

Edit: Just some changes.

[Forge]

I was always told that 1 was not a prime number, since it is also a square number...

Still, Miri was right - i means imaginary number - which is what you get from any root of a negative number.

I also checked that with my FOmar.

[Mirinee]

*Resists urge to post*...
*Fails*

Okay, firstly, I'm sorry for hijacking your thread, adrian, but I feel that people need to know the truth.

"Zero to the power of zero is unity" hurts my brain, but it's probably true, and it will hurt my brain a lot if you try to prove it.

Forge is right-- I think whiteninja meant to say that 1 is 'not counted as a prime number', (1 will always be an odd number).

Yes, it is indeed infinity when something divides by zero, which is undefined, and that's why it's called undefined .

An even power of any number is even

An even power of any number needs not be even:
e.g. 5^2=25 (25 is odd), but any integer power of an even number is even.

wheras an odd power of a positive number is positive and a of a negative is negative

All true. In fact, any positive power of a positive number is positive.

Negative number to an odd power example:
(-2)^3 = -8 (is negative)

The square roots of all negative numbers are imaginary, as are I think cubed roots, fourthed roots, fifthed roots, etc.

If you look at the previous example, you'll notice that the odd number roots of a negative number are not imaginary: they are negative.

e.g.
(-8)^(1/3) = -2 (Cube root of -8 is -2, which is not imaginary. Don't ask your calculator to verify this. It won't know. Ask FOmar.)

[whiteninja]

Forge is right-- I think whiteninja meant to say that 1 is 'not counted as a prime number', (1 will always be an odd number).

No, "I said what I said and I meant what I meant, an elephant's faithful 100%." (quote ~ Dr. Seuss)

I was always taught one is prime but not odd...

An even power of any number is positive

An even power of any number needs not be even:
e.g. 5^2=25 (25 is odd), but any integer power of an even number is even.

There, I did mean to say something different though. *goes to edit*

[Mirinee]

I was always taught one is prime but not odd...

I'm not a mathematician, so I can't really argue. What's its application as a prime but not odd?

[Shade]

*blinks*

what... my head hurts...
so 0 is unity and -1 is never square rooted and 1 is not really a number of and fixture at all... and...
its all so confusing...

[Forge]

Haha. Don't you just love this in depth mathematical philosophy, Shade?

I don't understand why one would be a prime number but not an odd number. The even numbers follow a very simple pattern - if it can be divided by two and come up with a whole number then that proves that the number is even.

Since a number can only be either odd or even (and these are mutually exclusive), and since 1 divided by 2 = 1/2 (meaning both a half and one divided by two) which is not a whole number means that 1 is not even, and therefore must be odd.

Could you explain the reasoning behind your teachings, whiteninja? You've confused me just a tad...

[whiteninja]

That is just what I was taught. "One is prime, but not odd." I don't get it either, and in fact it seems wrong; maybe my math teacher got it wrong way back when in 5th grade?

I also thought that even numbers were any numbers that ended in 2, 4, 6, 8, or 0 (excluding "0" itself), but from the way you said it, Forge, it sounds like it has to be an even integer. So numbers like 4.8372 would be odd, but I was taught they were even because they ended in an even (in this case "2").

So, now who wants to debate on the (ir)rationality of pi?

[Shade]

Haha. Don't you just love this in depth mathematical philosophy, Shade?

I don't understand why one would be a prime number but not an odd number. The even numbers follow a very simple pattern - if it can be divided by two and come up with a whole number then that proves that the number is even.

Since a number can only be either odd or even (and these are mutually exclusive), and since 1 divided by 2 = 1/2 (meaning both a half and one divided by two) which is not a whole number means that 1 is not even, and therefore must be odd.

Could you explain the reasoning behind your teachings, whiteninja? You've confused me just a tad...

no... i dont like it... lol