Does .99(repeating) = 1

Given that .111(repeating) = 1/9

.222(repeating) = 2/9
.333(repeating) = 3/9
.444(repeating) = 4/9

and on and on

would 9/9 equal 1 and .99(repeating)?

Yes

So if infinitely speaking a number can be “rounded” up…does 2 = 4

Try graphing it and you’ll have one answer.
Using some math I learned in grade 12 would also give you an answer but I’ve forgotten how to do that proof :embarrassed:

No.
9/9=1 - this is second grade mathematics, my niece is just going through this.
.999 repeating does not equal 1 nor does it equal 9/9.

Dolomite21 asked:

Can you provide a chain of reasoning similar to that in your first post to suggest that it might?

Let x = .99999…

10x = 9.99999…

10x - x = 9.99999… - .99999…

9x = 9

x = 1

QED

That wasn’t nice, Lib. Shame on you for playing nasty little games like that.

no, x = .99999…

Almost the same, but not. It will be forever under 1. Infinitely small as the gap may be, it still exists. For instance, does the matter in a black hole dissappear when it is formed?

Bad Lib, not supported anywhere, and not true besides.

There was nothing nasty about Libertarian’s proof. It is perfectly valid and 0.999… does equal 1. I wish people who know nothing about mathematics would content themselves with reading these threads rather than posting in them.

Give me a number between 0.999… and 1.0.

(We’ve been through this before. Do a search.)

There’s no gap. To invalidate the proof I gave, you have to find a flaw in the chain of deduction. Stories about black holes, however romantic and mysterious they may be, do not contradict the proof.

[deadpan]Maybe someone should ask James ‘Spaceman’ Driscoll about this. He’s an authority on the subject.[/deadpan]

d&r, sniggering

Nope. An infintely small value does not exist, it seems. Perhaps in theory, but not in practice.

Following the same “logic” will also prove that .333 repeating =1
Care to argue that one?

Also, if you allow changing the base of the numbers from ten, then you can prove that everything equals one. So much for a valid proof.

Sure. The number between 0.333… and 1.0 is 0.666… Therefore, 0.333… does not equal 1.0. As there is no number between 0.999… and 1.0, 1.0 is equal to 0.999…

so using that logic…would 7 also be the middle number

Following Libertarians logic:
Let x = .33333…

10x = 3.33333…

10x - x = 3.33333… - .33333…

3x = 3

x = 1

QED?
Something is fishy here.

Look here for a better proof.

This is why I said Lib’s proof was nasty. It shows the intended result, but also shows the same result in other conditions where it doesn’t apply.