Maths query

[CheeseSlice]

To make the 0.9999re-occurring you could try a subtraction

1 - 0.000000....1 (re-occurring 0's but with just a single 1 at the end)

Another way of thinking about this is that some indecisive twunt can't make their mind up when to stop and finally place the 1 at the end, and because they haven't made their mind up yet, the equation can never be evaluated.

Basically these re-occurring numbers aren't valid numbers, even if some maths idiot has come up with a fancy way to represent these with a dot above the re-occurring number. As Zeity says its just a decimal conversion problem from floating point. The decimal system (base 10) has no way of representing some floating points without decimal places going on forever, which is impossible to write down or for a computer to finish storing in memory.

[SpontaneousOrder]

It is not impossible to evaluate. It may be impossible to evaluate in a finite time by an iterative method, but that is not the same thing.

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

That has just evaluated it.

This is presuming that we are dealing with the Real Numbers. I could do you some other axiomatic systems if you like, with varying results.

You cheated. You did 1/3 = 0.333...
and then you completely discarded the 0.333... and did the next step using 1/3 (3 * 1/3 = 1).

I.e. 1/3 isn't a number - it's an abstraction.

[vwdan]

If you did a graph of it the lines would never meet but they would get so close that you could not tell the difference.

If it's impossible to extrapolate a difference between two things, then how can they be considered different?

As already posted, it's well accepted that 0.999... equals 1. There's not really a debate to be had.

[SpontaneousOrder]

If it's impossible to extrapolate a difference between two things, then how can they be considered different?

As already posted, it's well accepted that 0.999... equals 1. There's not really a debate to be had.

The debate is whether that equality is satisficing or absolute.

[expat]

To make the 0.9999re-occurring you could try a subtraction

1 - 0.000000....1 (re-occurring 0's but with just a single 1 at the end)

Another way of thinking about this is that some indecisive twunt can't make their mind up when to stop and finally place the 1 at the end, and because they haven't made their mind up yet, the equation can never be evaluated.

Basically these re-occurring numbers aren't valid numbers, even if some maths idiot has come up with a fancy way to represent these with a dot above the re-occurring number. As Zeity says its just a decimal conversion problem from floating point. The decimal system (base 10) has no way of representing some floating points without decimal places going on forever, which is impossible to write down or for a computer to finish storing in memory.

You can't do that, there isn't an end.

[vwdan]

The debate is whether that equality is satisficing or absolute.

There doesn't seem to be any debate over it in the maths world.

[expat]

You cheated. You did 1/3 = 0.333...
and then you completely discarded the 0.333... and did the next step using 1/3 (3 * 1/3 = 1).

I.e. 1/3 isn't a number - it's an abstraction.

I assert that these 3 identities are all self-evident, by definition:
Equation 1: 1/3 = 0.333...
Equation 2: 3 * 1/3 = 1
Equation 3: 3 * 0.333... = 0.999...

By Eq 1, the left side of Eq 2 = the left side of Eq 3.
therefore the right side of Eq 2 = the right side of Eq 3.
QED

[CheeseSlice]

I assert that these 3 identities are all self-evident what my casio calculator tells me, by definition:
Equation 1: 1/3 = 0.333...
Equation 2: 3 * 1/3 = 1
Equation 3: 3 * 0.333... = 0.999...

By Eq 1, the left side of Eq 2 = the left side of Eq 3.
therefore the right side of Eq 2 = the right side of Eq 3.
QED

FTFY

[VectraMan]

What's 1 - 0.9999999.... ? It can only be 0.0000000 recurring, which no matter how long you do it will only ever be zero. If something minus something is zero, the two somethings must be equal.

The more important question is how do I make my calculator say boobies?

[NickFitz]

I don't know why you're all still bickering about it. In case you missed it on the first page:

Simple arithmetic proof:

1 ÷ 3 = 0.333…
0.333… ✕ 3 = 0.999…

∴ 1 = 0.999…

Q.E.D.