Mathematical Oddity

A calculator tells you:

1/3 = .3333...

so

1 = .9999...?

 

no of course not

sit down and do it by hand and you'll quickly see why it comes out that way

if 1/3= 0.3 then it would be correct to assume that 1=0.9

but not when its a repeating, never ending decimal...it is MORE than .3, but less than .4

 

Who the hell sat down and invented math anyways?

 

From that answer: does that mean that 1 is MORE than 0.999.. but less than 1? Lol. Thank you Xelda, my mind has been fucked.

 

0.99999999...., with an infinite number of 9's is equal to 1. It's a fact that can be proven quite easily, but you need to use some limits and sum symbols. It's really not all that surprising if you understand the mathematical meaning of infinity.

 

Yup.

I was about to say, it's basically rounding error.

 

No, it's not. It's equal to exactly 1. No more, no less.

 

Syntax - I meant using a calculator. The memory can only go so far as to a bunch of digits, not the full sum. So 1/3 x 3 on a calculator gives the incorrect .99999

 

Well. Some calculators may do that (mine just gives 1). But 1.999.... is still equal to 1.

 

I think we need a proper mathematician in here to explain how 0.999..(to infinity) = 1.

 

OK.

Let x=0.9999999(etc),
then 10X=9.99999999(etc)
So
10X - X =
9.9999999999(etc)
-0.99999999999
=9

10X - X = 9X so 9X=9 or X=1.


This shows that infinitly repeating decimals are tricky as is anything involiving infinity.

 

i need some pot after i try to read this thread again.............

 

seriously, what shitty calculators u people must have, mine works fine
1/3 X 3 = 1

 

No, by that logic it would mean it's more than .9 but less than 1.2

 

What? Could you explain what you mean? I don't understand that at all.

If 1/3 = 0.33333....(infinity)
Then it seems that 3/3 = 0.99999....(infinity).

That is, 3/3 is more than 0.999999(etc) but less than 1, which is absurd.
If you can prove that 0.99999(to infinity) is equal to 1 then we can rest easy than 1 does in fact equal one. But it seems rather assumptive to state that an infinite decimal equals a whole, real number.

Ie. The number 29. Is it the same as 28.999999(to infinity), or is that wrong?
It seems wrong. One of those is infinite in length, and one of those is not.
Right?




Lol...

 

Lol.... wow, best explanation so far.

 

It's not assumptive. It has a formal, rigorous proof: but it requires some fancy symbols that are difficult to present on this board, and also won't be understood by people who didn't spend a lot of time studying mathematics (who should know this proof anyway).

It's right. The two numbers are the same. The thing is that the length of numbers is not really important / meaningful, especially when dealing with infinity. What is the size of the set of all real numbers? What is the length of an infinite ruler? You can't answer these questions. Even "infinity" is not a correct answer, because infinity is not a number.

Here's one way of looking at this:

You say "28.999999(to infinity)", but this is not formal notation. 28.9999.... is not formal either, as these dots are not formally defined. So really, when you say "28.999999(to infinity)" you are saying nothing other than 29.

 

Ok

Right,

That was a good explanation! But still, when you insert for X, you see that 9X is actually only 8.999(etc), and it still seems presumptuous to call that 9. Lol

~Peace

 

Thank you, Syntax. I do remember seeing this proof, or this puzzle, before, but I still feel slightly mindfucked. Lol.

I understand that practically, calling an infinite 28.999.. a firm 29, makes sense. But in a more philosophical sense, you cannot say that an infinite decimal equals a real number. By definition of infinity, it never reaches the mark, right?
~Peace

 

Simple.. .3 * 3 = .9, .4 * 3 = 1.2 1/3 is less than .4, but more than .3, so 1 is less than 1.2, but more than .9