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

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Originally Posted by Kardan

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



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.

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So by that logic, does 1.999 recurring = 2?

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Originally Posted by Intersocial

So by that logic, does 1.999 recurring = 2?

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Yes.

x = 1.999...
10x = 19.999...
10x - x = 9x = 18
9x / 9 = x = 2
x = 1.999... and x = 2

Works with every number that has infinite 9's after the decimal point.

Can also work in other examples...

E.g: 0.2499999... = 0.25

Quote:

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Originally Posted by Kardan

Yes.

x = 1.999...
10x = 19.999...
10x - x = 9x = 18
9x / 9 = x = 2
x = 1.999... and x = 2

Works with every number that has infinite 9's after the decimal point.

Can also work in other examples...

E.g: 0.2499999... = 0.25

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Out of 11 years of maths at school, this is the only thing in maths that has genuinely interested me haha. It's still such a wonderful occurrence though how 1 number directly equals another without needing alteration. At least you managed to explain it simply as opposed to those sites full of debates over it haha.

Quote:

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Originally Posted by Intersocial

Out of 11 years of maths at school, this is the only thing in maths that has genuinely interested me haha. It's still such a wonderful occurrence though how 1 number directly equals another without needing alteration. At least you managed to explain it simply as opposed to those sites full of debates over it haha.

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This is the thing though, you say "How one number equals another"... But they're not different numbers. They are the same number. Like saying 1/2 = 0.5 = 5/10. It's 0.999... = 1 = 10/10 = 456/456

A number cannot equal a different number :)

Quote:

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Originally Posted by Kardan

This is the thing though, you say "How one number equals another"... But they're not different numbers. They are the same number. Like saying 1/2 = 0.5 = 5/10. It's 0.999... = 1 = 10/10 = 456/456

A number cannot equal a different number :)

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This is driving me round the bend ;l. So it's basically 1 number written in a different format? Dear God just say yes, or I'll be confused as to how you can write "0.9999" and then "1" and say you have 1 number :P I get the rest though haha.

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Originally Posted by Intersocial

This is driving me round the bend ;l. So it's basically 1 number written in a different format? Dear God just say yes, or I'll be confused as to how you can write "0.9999" and then "1" and say you have 1 number :P I get the rest though haha.

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Yes :)

People are fine accepting that numbers have numerous forms as a fraction (E.g: 2 = 4/2, 8/4), but people don't seem to accept that numbers can have numerous forms as a decimal :)

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Originally Posted by Rixion

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

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No, it is exactly 1. There is NO difference at all.

0.999... is exactly the same as the number 1. As I said earlier, try and think of a number between 0.99... and 1. There is no such number therefore they are the same.

There is no number that lies between 6.2 and 6.2, therefore they are the same number.

0.333 = 1/3. 1/3 * 3 = 1, therefore 0.333 * 3 also equals 1.

The difference between 0.999.. and 1 is SO minimal that it is non existant 8)

But there is a minimal albeit tiny difference but it's that small it isn't considered.

There isn't a difference, they are exactly the same thing (h)

The gap between 0.99999... and 1 is so infinitely small that it is non existent I guess.

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Originally Posted by Rixion

But there is a minimal albeit tiny difference but it's that small it isn't considered.

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There is no difference, that's the whole issue that people have with this statement :P