.99999999 = 1?

It's misconception # 2 in the video:



His rationalization is fairly simple.

We know that .33333333 = 1/3
We know that 1/3 + 1/3 + 1/3 = 1
Hense .999999999 = 1

I never really put this into perspective but it becomes increasingly complex the more I think about it. If we look at 1 as a distance, such as an inch, is .99999999 actually a real number? You could magnify the inch infinite times to see how close .99999999 is to it. It should always be close but never quite reach right? So no, it's not equal to 1. On the other hand, I never noticed the way his equation worked before. How can the math with the fraction work, when the math with the decimals produces a different answer? Is it possible that we've made a fundamental flaw in how we understand math?

I appologize for not knowing how to scribe a vinculum on an iPad. (We are discussing repeating decimals, no need to clarify it in your posts.)

 

i've seen this thread before and have seen many claim .9999999... = 1. My common sense meter says they are wrong.

 

http://en.wikipedia.org/wiki/0.999...

 

I'm even more confused now

 

Not in DUI court

 

Yeah the overall gist is that .99999 = 1 and that we're all just too stupid to understand it.

Or nerds are trolling us all.

 

I know it's accepted, but I still recognize .333 repeating as being rounded. Decimals are rounded, while fractions are exact, IMO.

I guess if the string of numbers is truly infinite then there is no way to round it.

 

.99999999 continuing isn't a real number. It is just constantly approaching a certain number which is one so for all purposes, it equals one if you are going to treat it as a real number

 

but if it never ever reaches 1....

 

Repeating

 

that was meant to be all caps, so


REPEATING

 

.3333333... isn't 1/3

 

Then your common sense is wrong. But this isn't the type of question that common sense really applies to, so you're still cool.

But it does, in a way. That's the difficulty that people have with the concept of infinity. "Common sense" tells you that there is an end 9, when there's not.

 

Hmmm, interesting.
It's weird, you could take 1/3 of an inch and measure an exact distance, but in theory it's impossible to do in decimal form, even though its an exact measurement. However a fraction for 1 is written 1/1, 2/2, ect....but you will never get .9999999 doing the actual division. You do for 1/3.

 

my common sense doesnt tell me there is an end to 9. It tells me it is infinite and it goes on forever. But it also tell me that it never ever at any point reaches 1 thus it does not = 1

 

In math, no.

But in life I wouldn't mind if a few atoms were missing in my pudding.

 

What he said.

If you accept that .3333333=1/3, then of course 3x that would be =1. But it's not.

 

I've seen these threads in other forums, and they all turn into shitstorms.

1/3+1/3+1/3=1, not .999(repeating)

Which goes to reason that 1/3 is not .333(repeating).

 

I carry this motion forward and decree most of you 'dumb'.

 

If you were doing it in decimal form, you would be using the metric system.