Maths.. thing. .9999... = 1

[MKR&*42]

Someone told me about this irl after discovering it online a few months back, I thought it was pretty nifty tbh.

The argument goes something like this:

0.333… is 1/3, right? Well 1/3×3=1. But surely 0.333…x3=0.999…! Therefore, by one or another form of the transitive property, 0.999…=1!

Basically,the argument is; if 1/3 = 0.3333 recurring, 2/3 = 0.66666 recurring and 3/3 = 0.99999 recurring, yet 3/3 is a "whole" (1), does that make 0.99999 recurring = 1 without any form of rounding up. I've read through a few approaches to it online and it has caused some interesting debates haha.

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• http://boards.straightdope.com/sdmb/...9&pagenumber=1
• http://www.straightdope.com/columns/...y-doesnt-999-1
• http://sciencedefeated.wordpress.com...11/05/09999-1/
• http://www.askamathematician.com/201...ly-equal-to-1/
• http://www.xamuel.com/why-is-0point999-1/

Was hard to get my head around when I first found out :hmm:

Thread moved from 'Discuss Anything' by Matts (Forum Moderator)

[Empired]

This is really confusing but I do at least half understand. I've never even thought of that before ;o

[Munex]

I understand this and I asked my math teacher in GCSE. He says 0.999 recurring is basically so infinitely close to 1 that they call it 1. It's literally INFINITELY close to 1.

0.999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999 is nowhere near the number it truly is.

[Matthew]

Basically, can you think of a number between 0.99... and 1? No you cannot, therefore they are the same. Its the same with 0.4999..., there is no number between 0.499 and 0.5 therefore 0.499 and 0.5 are effectively the same thing.

Its like saying there's no number between 5 and 5, therefore they must be the same. There's no number between 106 and 106, therefore they must be the same etc.

[Smurfed-]

I'm sorry but my brain has just turned to mush.

[Kardan]

You can mathematically prove that 0.999... recurring is equal to 1.

Example:

Lets say we have x = 0.999... recurring.
Therefore 10x = 9.999... recurring.
10x - x = 9, so 9x = 9
Divide through by 9, and x = 1
If x = 0.999... recurring and x = 1, then 0.999... recurring = 1

This is very basic and simple really.

[Tarmu]

Heard about this from a video @0.37 http://www.youtube.com/watch?v=xM3_ltur0lo

[Rixion]

It's not exactly 1 but it's close enough to be considered enough, the difference is that minimal.

[MKR&*42]

You can mathematically prove that 0.999... recurring is equal to 1.

Example:

Lets say we have x = 0.999... recurring.
Therefore 10x = 9.999... recurring.
10x - x = 9, so 9x = 9
Divide through by 9, and x = 1
If x = 0.999... recurring and x = 1, then 0.999... recurring = 1

This is very basic and simple really.

Hey, not to start with

I like your explanation though haha, still confuses me (not "confuses", I can't think of a word) as to how one number can directly equal another.

[Kardan]

It's not exactly 1 but it's close enough to be considered enough, the difference is that minimal.

It IS exactly 1. That is the point of the whole confusion surrounding it.

Hey, not to start with

I like your explanation though haha, still confuses me (not "confuses", I can't think of a word) as to how one number can directly equal another.

Try not to think of it as 0.999... = 1, but that 0.999... is just another way of writing 1, as they are the same.

Like a stroller and a pram are the same thing.