LLD101

[EMP]

When I was taught Algebra II, I learned that there are more irrational numbers than rational numbers; there are more whole numbers than natural numbers; there are more real numbers than irrational numbers, rational numbers, and so forth. At that time, it made sense, and I accepted it.

Now that I think about it, the sets of rational numbers and irrational numbers should equal because numbers stretch on infiniately. So, there are an infinite amount of rational numbers. Irrational numbers also have an infinite number of numbers because it can also stretch into the infinite scale by decimals. Am I correct? In essence, there are the same amount of numbers in irrational numbers and rational numbers.

What about whole numbers and natural numbers? Whole numbers include the number "0", a number that natural numbers does not include. So, the number of whole numbers is "infinite + 1" while the number of natural numbers is simply "infinite." But what is "infinite + 1"? If the numbers reach such a big value, then the 1 shouldn't even matter any more, right? So does the number of whole numbers equal the number of natural numbers?

[Goky]

[B[x]]

[Wank]

Eh I'm in algebra II right now in my sophmoore year and we are going over that. Anyways, is there a reason why 2 negatives = a positive? Every time I ask my teacher they dont respond =.="

[Roy]

(-a) * (-b) = (-1) * a * (-1) * b

= (-1)*(-1) * ab

= 1 * ab

= ab

Thus, (-a) * (-b) = ab -- in other words, two negatives equal a positive.

[Wank]

I dont get it, I know that when you multiply a negative by a negative you get a positive, I just dont understand why.

P.S. I'm the kid in class that has 100 questions about everything

[Goky]

[EMP]

[Icanneverwin]

Heres one for you. I love this "1" heh.
where .9999999999(infinite) = 1

.999999(repeating) = x

Times both side by 10 so we get
9.99999(repeating) = 10x
since originally x = .999999(repeating)

just subtract x and/or .999999(repeating) on both sides and we get
9 = 9x
divide 9 by both sides and zomg x = 1 when it was originally .9999?!

Yes our 10 decimal system is screwed.

[Knifer]

you cant subract x, its being multiplied to 10

9.99999(repeating) = 10x

divide by x

9.99999(repeating) over x = 10

.999999(repeating) = x

10=10

[Goky]

You're both making it way too complicated.

(1/3) = 0.333333 (repeating)
0.3333333(repeating) x 3 = 0.99999 (repeating)
(1/3) x 3 = 1
Therefore, 0.99999 (repeating) = 1.

[Knifer]

[ATOMICMAN]

[Goky]

Oh, I thought you were trying to use that as a standalone proof (on top of his but with the correct algebra) which is just sort of complicated way of going about everything. I wasn't trying to be rude.

Mine wasn't exactly complicated, considering the easiest way to make the connection for someone who doesn't know much about math is by using the fact that 1/3 = 0.3333 (repeating) which is a pretty well known thing.

But you can LOL if I really hurt your feelings or something.

[EMP]