1.3333.. does NOT equal 4/3!

[Jessweeee♪]

This is what 3/10 looks like on paper.

[Tavrobel]

This is what 3/10 looks like on paper.

Thanks for the approximation and using the rules of significant figures.

Continuing on...

While we're on the subject of math, what does any number with an exponent of zero equal one instead of zero or that same number?

An exponent is really division/multiplication, except in this case, an exponent is a multiplied number multiplied many times. So 4² is 16 (4*4), or 6³ is 216 (6*6*6), or can be expressed as 6¹⁺¹⁺¹. Simply put, exponents represent how many times a number is multiplied by itself. Is it still not itself when it is alone?

Exponential numbers can be modified by adding and subtracting, a shortcut for signifying that a number can be multiplied that many number of times. There are such things as identities, numbers you use to keep a number that you have. For exponents, an identity is anything to the X¹ == X. Exponents already use to the first power as equalling itself. Addition uses N+0 == N, N*1=N, N¹ == N.

Let's take a number, a variable: (A)
It can equal anything besides zero.

Second variable: (n)
This is our exponent.

Aⁿ/Aⁿ, is the same as saying A^{n - n}, since we can manipulate exponents however we want.

What happens when we subtract any number from itself? We get zero, the additive identity. After all, A + 0 is still A. Applied to division, A^{n - n} is the same as A⁰. When you divide anything by itself, it equals one. Therefore, A⁰ == 1, as long as A != 0.

There's a multiplicative proof using algebra, but the divison proof is easier to remember, even if it does use more mathematical theory than the other.

[oddler]

Math is fun...

Oh, yeah!

While we're on the subject of math, what does any number with an exponent of zero equal one instead of zero or that same number?

x to the n-th power equals x times (x to the n-th minus one power).
So, 5 cubed is equal to 5 times (5 squared) and 5 squared is equal to 5 times (5 to the first power).
Therefore, 5 is equal to 5 times (5 to the zero power).
5 = 5 x 1


Edit: Tav.

[Tavrobel]

Edit: Tav.

I prefer the division, since it's more familiar to me, although I guess I had elements of both.

[Shoeberto]

I saw a proof of why .9999... = 1 before in calc but I totally forget it now ?

[rubah]

Why wouldn't it be true in other number systems? I just tried it in base 2 and it seems to be pretty much the same.

Decimal, the ".999. . . ."

Fractions, the "3/3"

[Meat Puppet]

Why don’t you just ask God?

[Anaisa]

Oh not this again! Maths is the epitome of boring.

[Jessweeee♪]

Thanks, Tavrobel n.n

My teacher just did the table thing and said it had to be one otherwise the pattern wouldn't fit, and offered no other explanation. I thought that was silly, but it gave me a headache thinking of a broken pattern like that :\

[Tavrobel]

Why wouldn't it be true in other number systems? I just tried it in base 2 and it seems to be pretty much the same.

Most odd number systems (such as x/13), certain even numbers with an odd number prime root, and prime numbers have never-ending approximations for a fraction value. Not that I needed to tell you that, but it does hold true.

[Firo Volondé]

To answer the title, it does. I don't remember the proof exactly, but I think it was this.

1/9 = 0.1111...
=> 10/9 = 1.111...
=> 90/9 = 9.999...
=> 9/9 = 0.9999...
=> 1 = 0.9999...

Or something like that. This exact wording actually doesn't hold up because the first line assumes that my conclusion is already correct...

[Tavrobel]

1/9 = 0.1111...

I like how people continue to oversimplify the relationship between ratios (4/3) and approximations (1.34).

[Mittopotahis]

alright, let's let x = .999999...
x = .999999...

I trust everyone agrees that if we times it by 10, we're gonna get 9.999999...
10x = 9.999999...

Now we'll find 9x. To do that, we just simply take 10x, and minus 1x.
10x - x = 9.999999 - .999999
9x = 9.

Divide both sides by 9 to find x by itself...
9x/9 = 9/9
x = 1

If we remember back to the start, we let .999999... equal x. So lets substitute that back in. x = .999999...

.999999... = 1.

And there you have it. .999999... DOES equal 1. Solid mathematical proof.

[Cz]

Oh not this again! Maths is the epitome of boring.

This. If you're going to make fun of someone's opinions, can't you at least make them interesting ones?

[.:kerrod:.]

alright, let's let x = .999999...
x = .999999...

I trust everyone agrees that if we times it by 10, we're gonna get 9.999999...
10x = 9.999999...

Now we'll find 9x. To do that, we just simply take 10x, and minus 1x.
10x - x = 9.999999 - .999999
9x = 9.

Divide both sides by 9 to find x by itself...
9x/9 = 9/9
x = 1

If we remember back to the start, we let .999999... equal x. So lets substitute that back in. x = .999999...

.999999... = 1.

And there you have it. .999999... DOES equal 1. Solid mathematical proof.

YES! that is correct *sniff* that is so beautiful...i learned that in maths c (the hardest and optional maths at my school) a while ago and it brought a tear to my eye when i saw it...thank you...you are exactly right, btw: i did have a WHOLE webpage proving it but i lost it

EDIT: here's a page, not the one i was thinking of, but very close to it: Point nine recurring equals one @ Things Of Interest