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## Does 0.9999(repeating) = 1?

Yes 705 56.9%
No 578 46.65%
Voters 1239 .

### Does 0.9999(repeating) = 1?

Kaolla

Senior Member

Quote:
Crowcide:
So your big qualm is that we write decimal notation? You get decimals are just notation and definition.

decimals are a notation in which infinite repeating numbers tend towards the values expressed in other fractional notations or functions. current math has defined these repeaters to be equal for convenience.

PeacÃ«

Senior Member

Well I just discovered that some of what I'm arguing has a name: Hyperreals.

I would argue that Reals cannot be complete without hyperreals (which is why I stated my first comment). Hyperreals allow for 0.999... not equal to 1.

Assuming the Archimedean principal is wrong, see pages 63-66: http://math.coe.uga.edu/TME/issues/v21n2/5-21.2_Norton%20&%20Baldwin.pdf

Born too late again, drats.

Crowcide

Senior Member

Quote:
Folly Inc:

Do you agree that .999 does not -always- equal 1 in a linguistic comparison?

Of course I agree with that, they are expressed with different symbols

Crowcide

Senior Member

Quote:
Peacë:
Well I just discovered that some of what I'm arguing has a name: Hyperreals.

I would argue that Reals cannot be complete without hyperreals (which is why I stated my first comment). Hyperreals allow for 0.999... not equal to 1.

Assuming the Archimedean principal is wrong, see pages 63-66: http://math.coe.uga.edu/TME/issues/v21n2/5-21.2_Norton%20&%20Baldwin.pdf

Born too late again, drats.

So your point is based on if you assume the axioms for a system are wrong.

You get if the axioms are "wrong" I.e. lead to a contradiction you can prove anything true in the system

An axiomatic approach to the reals is mostly a short cut to avoid all the hassle with generating it from the set theory axioms, something you can do completeness included

Folly Inc

Senior Member

Quote:
Crowcide:
So your point is based on if you assume the axioms for a system are wrong.

You get if the axioms are "wrong" I.e. lead to a contradiction you can prove anything true in the system

An axiomatic approach to the reals is mostly a short cut to avoid all the hassle with generating it from the set theory axioms, something you can do completeness included

So I thought about this last night, before I fell asleep. I'm probably wrong and don't understand base numbers the way I think I do, but I thought I'd throw it out there anyway.

If we assume a Base 1 numerical system, wouldn't X = (1/y) 1 be mathematically sound? the equation is solely meant to define 1 as a number, so it doesn't work with other numbers. But it does work with one.

Crowcide

Senior Member

Quote:
Kaolla:
decimals are a notation in which infinite repeating numbers tend towards the values expressed in other fractional notations or functions. current math has defined these repeaters to be equal for convenience.

Who should get to decide what numbers are equal too? You or current math.

Crowcide

Senior Member

Quote:
Folly Inc:
So I thought about this last night, before I fell asleep. I'm probably wrong and don't understand base numbers the way I think I do, but I thought I'd throw it out there anyway.

If we assume a Base 1 numerical system, wouldn't X = (1/y) 1 be mathematically sound? the equation is solely meant to define 1 as a number, so it doesn't work with other numbers. But it does work with one.

The base 1 number system is essentially just making hash marks and i'm fairly sure it only related to the natural numbers.

Kaolla

Senior Member

Quote:
Crowcide:
Who should get to decide what numbers are equal too? You or current math.

we went through this already. logic

Crowcide

Senior Member

Quote:
Kaolla:
we went through this already. logic

logic disagrees with your interpenetration of decimals. You looked up axioms yet?

Kaolla

Senior Member

Quote:
Crowcide:
logic disagrees with your interpenetration of decimals

why would it?

i would assume this is the same logic you use to make 10 / 3 = 3