0.999...=1 and why people believe it is false.

[Gmesh]

Just a thought but 1/3 does not exactly equal .333...

[Kiriyama]

Well, 1/3 is continually going on, infinitely as 0.333... we haven't discovered the point where it equates to being that 1/3 gives a complete number, simply because we either don't know how, or we do not have the time to discover it.

 

 

 

If you tried to write infinity as a number, not a symbol, then it is forever ongoing, you never stop. That is the idea behind 0.333...

[Gmesh]

Well, 1/3 is continually going on, infinitely as 0.333... we haven't discovered the point where it equates to being that 1/3 gives a complete number, simply because we either don't know how, or we do not have the time to discover it.

 

 

 

If you tried to write infinity as a number, not a symbol, then it is forever ongoing, you never stop. That is the idea behind 0.333...

 

 

 

Thats my point lol :lol:

[Kiriyama]

I thought you're point was that there was no way it could equate to that.

 

 

 

Must have read it wrong, my apologies. But yeah, I agree with you. However, its easier just to agree with people on that. I'm more likely to fail Higher Maths if I don't accept this as a rule, than if I do. Its a trivial matter that is debated too much. Its more convient to put 1/3 as 0.333 when needed, cause hell, you're answer is going to be close enough to the real thing.

 

 

 

I mean, 1/3 of 6 is 2. 6*0.333 is 1.998. ITs a pretty damn close answer that most people will just write as 2, depending on how you need to do it.

[Cynic]

The way I see this problem is:

 

 

 

1/3=0.333....

 

(1/3)*(3/1)= 3/3= 1

 

WHICH IS THE SAME AS

 

0.333....*3=0.999....= 1

 

 

 

There is this one REALLY annoying kid in my grade that normally is very rational, but he just can't bring himself to believe this. It gets annoying when you are right and everyone else thinks you are wrong.

[Zimbu]

Just a thought but 1/3 does not exactly equal .333...

 

What do you mean? 0.333... and 1/3 are exactly the same number. I think the most simple way to prove it would be 0.333...=3/9=1/3.

 

Well, 1/3 is continually going on, infinitely as 0.333... we haven't discovered the point where it equates to being that 1/3 gives a complete number, simply because we either don't know how, or we do not have the time to discover it.

 

 

Idk if I read this correctly, but the fact that 0.333... is the same number as 1/3 has nothing to do with not having time or not knowing how to discover something about the number. All we need to know is that 0.333... has 0 in the integral part and an infinity of 3's in the fractional part of the number.

 

Its more convient to put 1/3 as 0.333 when needed, cause hell, you're answer is going to be close enough to the real thing.

 

 

 

I mean, 1/3 of 6 is 2. 6*0.333 is 1.998. ITs a pretty damn close answer that most people will just write as 2, depending on how you need to do it.

 

How I was taught to deal with repeating decimals: A common way to represent a repeating decimal is a line or dot over the repeating sequence of numbers, for example or 0.(9), so you don't have to use 0.333 to represent 1/3. Outside of mathematics in for example natural sciences, however, it's not a good idea to use any representation that would refer to an infinite accuracy. So a car moving at 120km/h in a physics calculation is a car moving at 33.333m/s even though 120/3.6=33.333...

[wild_goat_14]

Now to convince everyone that 1/0 =/= infinity.

 

 

 

Chuck Norris can divide by zero.

 

 

 

But seriously, I dare you to slice a pizza into 0 pieces.(And eating it doesn't count)

[brunokiller]

Now to convince everyone that 1/0 =/= infinity.

 

 

 

Chuck Norris can divide by zero.

 

 

 

But seriously, I dare you to slice a pizza into 0 pieces.(And eating it doesn't count)

 

 

 

1/0 = infinity

 

 

 

thus

 

infinity x 0 = 1

 

 

 

We also know 2 x 0 = 0

 

 

 

So

 

infinity x 0 x 2 = 1

 

 

 

(infinity x 0) x 2 = 1

 

 

 

(1) x 2 = 1

 

 

 

2 = 1

 

 

 

Chuck Norris can also transform numbers.

[Kiriyama]

Now to convince everyone that 1/0 =/= infinity.

 

 

 

Chuck Norris can divide by zero.

 

 

 

But seriously, I dare you to slice a pizza into 0 pieces.(And eating it doesn't count)

 

 

 

1/0 = infinity

 

 

 

thus

 

infinity x 0 = 1

 

 

 

We also know 2 x 0 = 0

 

 

 

So

 

infinity x 0 x 2 = 1

 

 

 

(infinity x 0) x 2 = 1

 

 

 

(1) x 2 = 1

 

 

 

2 = 1

 

 

 

Chuck Norris can also transform numbers.

 

 

 

You added in brackets to make 2 = 1.

 

 

 

infinty*0*2 = 1

 

 

 

infinity*(0*2) = 1

 

 

 

infinity*(0) = 1

 

 

 

See? I ended up back where I wanted to. Just like how you ended where you wanted to.

 

 

 

However, you cannot combine them, as they do not equate the the same originally.

[Zierro]

What do you mean? 0.333... and 1/3 are exactly the same number. I think the most simple way to prove it would be 0.333...=3/9=1/3.

 

 

 

That doesn't prove it. It just begs a new question: Does 0.333... = 3/9?

[wild_goat_14]

Now to convince everyone that 1/0 =/= infinity.

 

 

 

Chuck Norris can divide by zero.

 

 

 

But seriously, I dare you to slice a pizza into 0 pieces.(And eating it doesn't count)

 

 

 

1/0 = infinity

 

 

 

thus

 

infinity x 0 = 1

 

 

 

We also know 2 x 0 = 0

 

 

 

So

 

infinity x 0 x 2 = 1

 

 

 

(infinity x 0) x 2 = 1

 

 

 

(1) x 2 = 1

 

 

 

2 = 1

 

 

 

Chuck Norris can also transform numbers.

 

 

 

Prove that 1/0 = infinity.

 

 

 

And anything x 0 = 0. Infinity times 0 would equal 0.

 

 

 

So(even though it would still be mathematically incorrect because 1/0 =/= infinity(IMO, because I have no logical reason to believe this yet)), you have idioticly tried to say that this equation can come to 2=1 instead of 0=1. Nice one.

 

 

 

Also, division by 0 is a concept that I can't understand. Divide something into 0 parts? You can't.

 

[hide=OH NO.][/hide]

[fastortoise]

Just thought of something..

 

can anyone here think of a number between 0.999..(repeating) and 1?

 

:)

[walka92]

Just thought of something..

 

can anyone here think of a number between 0.999..(repeating) and 1?

 

:)

 

there is none. thats the point

[Kiriyama]

Just thought of something..

 

can anyone here think of a number between 0.999..(repeating) and 1?

 

:)

 

 

 

Infinity doesn't end, it is not a tangible answer.

 

 

 

Therefore, I say you can just keep on throwing on another 9. It'll never end anyway since you always get a new digit.

[fastortoise]

Just thought of something..

 

can anyone here think of a number between 0.999..(repeating) and 1?

 

:)

 

 

 

Infinity doesn't end, it is not a tangible answer.

 

 

 

Therefore, I say you can just keep on throwing on another 9.

 

Well, you can't add another 9 to the end of a decimal number going to infinity...That's why it's infinity #-o

[Kiriyama]

Yes, but infinity is not a real number anyway.

 

 

 

Its continually ongoing, hence you can always add another 9.

[fastortoise]

Yes, but infinity is not a real number anyway.

 

 

 

Its continually ongoing, hence you can always add another 9.

 

So with that reasoning,

 

0.9999... < 0.9999...9 < 1

 

The three dots represent the infinite number of nines, and the extra 9 'after' the infinite number of nines represented by "..." is the extra 9 you claim to have added.

 

But you do realize, those two first numbers on the left are the same number, right?

 

 

 

If you finally figured it out, you'd find

 

0.9999... < 1 is not possible because there is simply no number that separates them. They are equal.

[meol]

Yes, but infinity is not a real number anyway.

 

 

 

Its continually ongoing, hence you can always add another 9.

 

That's the problem with your reasoning. 0,9... does not mean you have 0,9 then 0,99 and then 0,999 and so on. It means there is already a string of nines of infinite length, and the ellipses indicate it already being infinite. It's a number, not a process. There is no last 9 "at infinity", so you can't simply add another digit to it.

[Kiriyama]

Yes, but infinity is not a real number anyway.

 

 

 

Its continually ongoing, hence you can always add another 9.

 

That's the problem with your reasoning. 0,9... does not mean you have 0,9 then 0,99 and then 0,999 and so on. It means there is already a string of nines of infinite length, and the ellipses indicate it already being infinite. It's a number, not a process. There is no last 9 "at infinity", so you can't simply add another digit to it.

 

 

 

But it can't exactly end either. So the reasoning there is no number between makes little sense.

 

 

 

Because surely, you'd need an end to make such an assumption.

[mistywerty]

Look at it this way:

 

 

 

1 / 3 = ? = 0.333...

 

 

 

0.333... x 3 = 1 = 0.999...

[20Rice04]

0.9999...... is reccuring, unless it is STATED there is an endpoint (or there is no dot above the end number - one which indicate it is infinitely reccuring) then to graph this point you would not draw a dot at point 1. It's asymptotic :)

 

 

 

Think of a frog hopping a pond. If the pond is one metre wide and the frog hopes 0.5 metres, then 0.25 metres, then 0.125 metres etc etc, it will theoretically NEVER reach the other side of the pond.

[brunokiller]

[hide=]

Now to convince everyone that 1/0 =/= infinity.

 

 

 

Chuck Norris can divide by zero.

 

 

 

But seriously, I dare you to slice a pizza into 0 pieces.(And eating it doesn't count)

 

 

 

1/0 = infinity

 

 

 

thus

 

infinity x 0 = 1

 

 

 

We also know 2 x 0 = 0

 

 

 

So

 

infinity x 0 x 2 = 1

 

 

 

(infinity x 0) x 2 = 1

 

 

 

(1) x 2 = 1

 

 

 

2 = 1

 

 

 

Chuck Norris can also transform numbers.

 

 

 

Prove that 1/0 = infinity.

 

 

 

And anything x 0 = 0. Infinity times 0 would equal 0.

 

 

 

So(even though it would still be mathematically incorrect because 1/0 =/= infinity(IMO, because I have no logical reason to believe this yet)), you have idioticly tried to say that this equation can come to 2=1 instead of 0=1. Nice one.

 

 

 

Also, division by 0 is a concept that I can't understand. Divide something into 0 parts? You can't.

 

[hide=OH NO.][/hide]

 

 

 

 

 

Here, have a good read.

[walka92]

Q: How many mathematicians does it take to screw in a lightbulb?

 

 

 

A: 0.999999.

 

>_>

 

 

 

 

 

 

 

also, does it really matter? personally i take the =1 side, but if i was challenged on it i wouldnt bother defending it because i honestly see no point

[Sly_Wizard]

So, what is 1.111... equal to?

[Rebdragon]

So, what is 1.111... equal to?

 

10/9.

 

 

 

Please don't continue.