0.99999999.......

[Franzl]

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

[Franzl]

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

Fun isn't it?

f(x) = 1 / x², a lot of people would say, never touches the x-axis, but only gets closer and closer to it.

It does, though, in theory. Under the same principle as the original question here, the function is considered to be infinitely long, and thus it also becomes infinitely close to the x-axis

[Franzl]

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

Fun isn't it?

f(x) = 1 / x², a lot of people would say, never touches the x-axis, but only gets closer and closer to it.

It does, though, in theory. Under the same principle as the original question here, the function is considered to be infinitely long, and thus it also becomes infinitely close to the x-axis

Still, 0.9999999... is not equal to 1. 

It is though

What's the difference between 0.9 and 1?
What's the difference between 0.99 and 1?
What's the difference between 0.999999999999 and 1?

If you truly assume an infinite number of 9s behind the decimal point....there can't be any difference between the two numbers.

To claim that the two numbers are not equal, you would have to assume a finite number of 9s behind the decimal point. But even 0.99999999999999999999999999999999999999999999 (and a million more 9s) is not equal to "0.99....".

[Franzl]

I do not dispute that 0.9999999... is indeed extremely close to one, but so say that it equals one make absolutely no sense whatsoever (but when has mathematics ever done that).  The difference will indeed be very (understatement) small, incalculable in fact, but no matter how much I look at it and think about it, it still strikes me as less than 1.  That said, if I don't need to be too precise when displaying the results of a calculation, I'll just treat it as one all the same (considering that when rounded you get 1), but I'll never be able to view it as equal to one though, that is, exactly equal.  I will look into this further.

OK, despite Libertas extremely nasty behavior....his math isn't wrong.

We agree that any number divided by itself equals 1, right? That can't be disputed! So 3/3=1.

Alright, now if you had to write 1/3 as a decimal number, what would it be? Is it 0.33? or 0.(lots of 3s?). It's clear that it's an infinite number of 3s behind the decimal point, correct?

But now if you multiply that number by 3, what do you get? wouldn't that be 0.333.... x 3 = 0.999...?


To argue that 0.999... is not equal to 1, you would have to dispute that 3 x 1/3 is equal to 1

[Franzl]

I have nothing to add to the thread, but I'd like to point out that if somone gets the answer "wrong" and it pisses you off and makes you think less of them, YOU ARE AN ASSHOLE!  Period, end of story.

Why would anyone think less of someone because they got mathematical theory wrong?

Personality and other qualities have nothing to do with mathematical ability.