0.999... = 1

That was actually written some times here before, and if you would click the link to wikipedia you would find 5 or 6 similar descriptions...

 

I know, i have read the whole topic...
But he was the one who posted an example last...

 

Tell me another pair of numbers that are equal in value and are written in exactly the same form (in this case, X.YY'), with different digits, which doesn't include any mathematical operations (since infinity isn't one either).

 

24.2789 is the same as 24.2788(999)....  The .999... is an infinite stream of numbers that can be placed at the end of most numbers. Infinte number streams can be placed a near infinite number of ways on most real numbers (ignoring things like pi, e and square roots) to create more than 1 way to write a number. Its just easier to use things like 1 or 24.2789 instead of a number with an infinte stream of repeating numbers behind it, just like its easier to use 1/9 instead of .111.... Does that answer your question?

EDIT: Damn I was confusing before....

 

Let me break it down for you
.1111111111111111111111111111111111111111111111= 1/9
.222222222222222222222222222222222222222222222 = 2/9
.3333333333333333333333333333333333333333333333 =3/9 =1/3
.
and so on
.
.9999999999999999999999999999999999999999999999 = 9/9 = 1

 

basically

1/3= .3333-
2/3=.6666-
1/3+2/3=3/3 .3333- + .6666- = .9999-
it makes sense in a funny way

 

Hey read sc2 forums for long time so decided to sign up (; so im new here as u can see.
Im unsure on this and can see both might be true. Just idea tad basic but i think does job,
If you had a special frog that could only jump half the distanced needed it would never reach its destination even if it had infinite number of jumps. eg for distance of 1m put at 0m at beggining 1st jump is 0.5m, 2nd 0.25, 3rd 0.125 etc it would never get to the finish line of 1m.

 

Thats actually false with an infinite number of jumps the frog would in fact reach its destination, it just couldn't with any fininte number or jumps. Once people start using infinitty the rules for some things change. For the record the frog situation can be modeled with a geometric series to show I am correct but I don't really want to try and type it all out.

 

So basically the infinite number of nines sort of round up the last finite digit to its next value.

I have to admit I'm a bit tired of this subject and I don't know what to make of this anymore
I still don't understand what that little extra is with infinity that allows us to denote the same number in two ways which is not there with finite decimals but I'll just put that down to me being too thick for maths.

 

heres an idea...

someone might say that 0.999999999... is just 0.0000000000000......1 shy of 1

does that mean that anything with an infinite number of zeros equals zero?
because if 0.9999... = 1 then 0.9999... + 0 = 1

 

They say 0.999... = 1 not 0.

 

He's saying how some people think that 0.999... is 0.000...1 less than one, not that 0.999... is equal to 0.

 

Ohh ok, i should have checked the word shy ...

 

It is most definitely an interesting subject

 

I'm surprised how many people have chosen 'No'. I bet a lot just voted without reading anything in the topic.
There isn't a way of proving that it doesn't equal one, and there are several proofs showing that it is exactly equal to one. Trying to prove that it doesn't is like trying to prove that five doesn't equal five or ten doesn't equal ten.

 

Yeah i (when the topic started) voted no, but the more research i made, the more i was going to yes, so i changed my vote to yes.

 

I was a bit like that. The first time I heard about it, I thought that it was ridiculous. However after seeing the proofs, it's undeniable. I don't see why people refuse to believe something that's been proven to be correct.

 

Get some statistics, 78% of all people trust you if you have statistics!

 

Of course! 0.9999999999 is not 1! But 0.9 recurving is 1. There has been few examples in this thread using algebra or fractions. The point is that you imagine the 0.9 recurving as 0.999*infinity*999. Well thats the problem. The number cannot end at 9, because it is infinite. It is against all our believes and logic I know and I dont expect anyone to believe that 0.9999... is 1. If you dont thats perfectly normal and I can tell that youre healthy and still quiet intelligent person.

But once you start studying maths properly, you find out that even things like 1+1 encounters immense problems and infact that saying 1+1=2 is not always correct.

 

___
if its like 0.999 with a bar on top (i think thats called recurving) the it would be equal to one

but 0.999999 itself isnt equal to one

i can prove that through sophisticated algebra but i have no time for that