Holes in mathematics

If you mean Calculus holes, which I'm positive you do; they are when it's nothing in the space, as if you go through a worm-hole and appear on the other side. It's a dimensionless area. It's 'undefined' in math for that reason. So whenever you simply an answer by factoring it, etc. and plug in your limit you always get a place where the denominator would be 0, the hole.

I think I'm awake enough to have not babbled.

 

No you idiot, any number divided by 0 is undefined. x/x = 1 but a non-permissible value for x is 0. This is called a domain restriction because division by zero is invalid and undefined, no matter what. Your conjecture that x/x = 1 works for all values of x EXCEPT 0. Got it? Good.

The definition of a rational number is a number with either a terminating OR a repeating decimal.

1/9 = 0.1111...
2/9 = 0.2222...
9/9 = 1

Again, you are not examining the evidence properly. Given that your friend's "proof" is likely the same old stupid 1 = 2 thing that is seen everywhere on the internet, I'll debunk it now:

a = b
a^2 = a*b
a^2-b^2 = a*b-b^2
(a+b)(a-b) = b(a-b)
(a+b) = b
a+a = a
2a = a
2 = 1

The error is in line 5. Because a-b = 0, you cannot divide both sides by a-b.

I suggest you educate yourself before formulating opinions on matters which have been proven, tested, and verified by people much smarter than yourself - and judging by your spelling and grammar, my guess is that being a whole lot smarter than yourself is not much of an accomplishment.

 

Looks nice, but is it correct? Of course not. for two reasons. The first is that once the recurring x number is multiplied by ten, it is no longer recurring. A number has been taken off the end of it, and put in front of a decimal point. Therefore...
x = 0.99999999
10x = 9.999999
10x - x = 8.999991
9x = 8.999991
x= 0.9999999


Just do it on a calculator, you will see exactly what I mean. Even if the original x was recurring, it would no longer be recurring once it was multiplied by ten. It doesn't work that way. You would get 8.9999999(a very large amount of 9's)1. That is the real answer to this "equation"
The other problem is that once it is stated that x=y, x cannot equal z at the end of the same equation. Once x is stated to have a specific value, it has to stay constant no matter what you do to it in that equation. And pretty much everyone fell for that, I'm surprised at you people >.>

 

Backstab and i love drugs are absolutely right, and Sythe isn't. Once a number is multiplied by ten, it can't be recurring any more

 

To ease all the he'd ache, remember that we live in a fractal world, not euclidian.

 

Explain 2nd?

 

TRY THIS ON THE CALC.

1 divided by 3 = 0.333333333 [recurring] and multiply that back again by 3 = 1.

Owned pls?

 

How about this;

If you apply a 2 D.P. rule

0.3333333333 Recurring = 0.33

However if you apply the same rule to 0.666666666 Recurring it = 0.67

:O This looks odd to me Increases by 34 as oppose to 33 when such a rule is applied

 

How does 0.666666666 reccuring = 0.67
Mind explaining?

 

2 D.P... Upper and Lower Boundaries. You round the third 6 up, to make 0.67, atleast that's what were taught in England. Then again, the cirriculum here is bs.

 

Nicely said.

 

Sometimes 0.9~ = 1 and sometimes it doesn't so who decided what it is, you do.

 

Do you have any grasp of math past 5th grade?

1/3 = .333 [recurring] yes
.333 [recurring] *3 = 1...

What exactly are you trying to say?

 

x = 0.99999999999 (recurring)
10x = 9.999999999 (recurring)
10x - x = 9 (Where does the 2nd variable come from)
9x = 9
x = 1

 

He subtracted .99999999999999999999 on both sides (legal math step).

He then substituted .999999999999999 for "x" another legal math step.

What's so hard?

 

Dude.. listen. Take a calculater and divide 1 by 3. Now, you know what you get, and then multiply what you got by 3. That = .9 recurring. Do it, and you'll see exactly what I'm trying to say.

 

Mine's right..

 

"Dude.. listen. Take a calculater and divide 3 by 1. Now, you know what you get, and then multiply what you got by 3. That = .9 recurring. Do it, and you'll see exactly what I'm trying to say."

Divide 3 by 1?

3/1 = 3. I'm assuming you meant 1/3, but I think that this mistake should stand as a testament to the fact that you don't know what you're talking about.

If you're using a junior high calculator, then 0.3333...*3 = 0.999 because of a limit to their precision. Use a TI-8x calculator (or virtually any other graphing calculator) and they will give you (1/3)*3=1.

 

Quite frankly, I DO know what I'm talking about, and don't have a junior high calc... so why get at me..? Nothing to do..?