Does 0.9999(repeating) = 1?

Yes 705 54.95%
No 578 45.05%
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Does 0.9999(repeating) = 1?

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Kaolla

Senior Member

01-28-2013

Quote:
Originally Posted by Crowcide View Post
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.


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Peacë

Senior Member

01-29-2013

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/v...%20Baldwin.pdf



Born too late again, drats.


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Crowcide

Senior Member

01-29-2013

Quote:
Originally Posted by Folly Inc View Post
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


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Crowcide

Senior Member

01-29-2013

Quote:
Originally Posted by Peac View Post
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/v...%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


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Folly Inc

Senior Member

01-29-2013

Quote:
Originally Posted by Crowcide View Post
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.


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Crowcide

Senior Member

01-29-2013

Quote:
Originally Posted by Kaolla View Post
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.


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Crowcide

Senior Member

01-29-2013

Quote:
Originally Posted by Folly Inc View Post
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.


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Kaolla

Senior Member

01-29-2013

Quote:
Originally Posted by Crowcide View Post
Who should get to decide what numbers are equal too? You or current math.
we went through this already. logic


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Crowcide

Senior Member

01-29-2013

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Originally Posted by Kaolla View Post
we went through this already. logic
logic disagrees with your interpenetration of decimals. You looked up axioms yet?


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Kaolla

Senior Member

01-29-2013

Quote:
Originally Posted by Crowcide View Post
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