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Does 0.9999(repeating) = 1?

Yes 705 56.9%
No 578 46.65%
Voters 1239 .

Does 0.9999(repeating) = 1?

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Folly Inc

Senior Member

01-24-2013

Quote:
Dobagoh:
no assumptions have been made, trollish idiot

Infinity is defined as assumption. It is impossible for infinity exist without assumption. So you're wrong, and an assumption is made.3

**post edit**

It is "impossible" for infinity to exist as a number representation of anything physical. To accommodate infinity you have to assume that infinity goes on forever in a real scenario. So it is -assumed- to be infinite.


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Dobagoh

Member

01-24-2013

Quote:
Folly Inc:
Infinity is defined as assumption. It is impossible for infinity exist without assumption. So you're wrong, and an assumption is made.

No it isn't.


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Folly Inc

Senior Member

01-24-2013

Quote:
Dobagoh:
No it isn't.


If so, prove to me that space is infinite.


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Crowcide

Senior Member

01-24-2013

Quote:
Folly Inc:
Infinity is defined as assumption. It is impossible for infinity exist without assumption. So you're wrong, and an assumption is made.3

**post edit**

It is "impossible" for infinity to exist as a number representation of anything physical. To accommodate infinity you have to assume that infinity goes on forever in a real scenario. So it is -assumed- to be infinite.

You're actually right, infinity exist because of assumptions. Those assumptions are the axioms of set theory and the basis of ALL math.

A big part of the confusion in this thread is people thinking that real life dictates how math works. This isn't true math exist independent of "the real world". We do math from axioms. If those axioms describe the real world we assume the results of math apply.


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Folly Inc

Senior Member

01-24-2013

Quote:
Crowcide:
You're actually right, infinity exist because of assumptions. Those assumptions are the axioms of set theory and the basis of ALL math.

A big part of the confusion in this thread is people thinking that real life dictates how math works. This isn't true math exist independent of "the real world". We do math from axioms. If those axioms describe the real world we assume the results of math apply.


But how do you think those Axioms were derived? like it or not, anything in this plane of existence is tied to reality in one way or another. Math was not something that popped into existence because someone liked the idea of numbers. It was practical to real life.

The point that .999... does not equal 1 simply because it -is not one- is true. You CAN say, that within the limitation of certain (and most) mathematics that .999... can equal 1 for the purpose of the equation.


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Crowcide

Senior Member

01-24-2013

Quote:
Folly Inc:
But how do you think those Axioms were derived? like it or not, anything in this plane of existence is tied to reality in one way or another. Math was not something that popped into existence because someone liked the idea of numbers. It was practical to real life.

The point that .999... does not equal 1 simply because it -is not one- is true. You CAN say, that within the limitation of certain (and most) mathematics that .999... can equal 1 for the purpose of the equation.

Something like .999... as you are thinking of it never occurs in the real world. It's a purely mathematical construct called a "geometric series", one which happens to equal 1. .999... does with absolute certainty = 1.

The historical tale of axiomatic systems is much much more complicated than you are painting it to be. There are plenty of other systems that don't relate very well (or at all) to real life. Take non-euclidean geometries, modal logic, any of the Zn groups, for example. Also when we try to tie math to the real world things often go horribly wrong, go read up on "russell's paradox". It arose because we tried to model set theory axioms off of what "made the most sense" in the real world. Originally one of the axioms of set theory was the axiom of unrestricted comprehension which makes tons of intuitive sense, sadly it turned out it wasn't mathematically valid and had to be replaced with schema of separation which makes very little sense in the real world.

Historically we originally did math off of common sense and intuition. With the belief that the only mathematical systems that were valid were ones that could be represented in reality. Slowly over time formal systems were adopted, and the view switched to the total opposite. Now pure mathematicians develop systems with no care or concern for what exist in the real world, then it's the applied mathematicians job to find a use for them.


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Kaolla

Senior Member

01-24-2013

Quote:
Crowcide:
You posited a belief. I asked you a question relevant to that belief that you most likely know will ultimately show you to be wrong


you're asking me if i know of whatever, and won't tell me why it's relevant. i KNOW it's a red herring so i'm ignoring it

if you wish to persist in this line of inquiry, you can explain it. if not, fine. you can give up

asking if someone knows something in the internet age is dumb, anyone can google what you're talking about. so it's obvious that you have an ulterior motive for trying to get me to acknowledge it.

i don't fall for 1990's message board deceptions


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Folly Inc

Senior Member

01-24-2013

Quote:
Crowcide:
Something like .999... as you are thinking of it never occurs in the real world. It's a purely mathematical construct called a "geometric series", one which happens to equal 1. .999... does with absolute certainty = 1.

The historical tale of axiomatic systems is much much more complicated than you are painting it to be. There are plenty of other systems that don't relate very well (or at all) to real life. Take non-euclidean geometries, modal logic, any of the Zn groups, for example. Also when we try to tie math to the real world things often go horribly wrong, go read up on "russell's paradox". It arose because we tried to model set theory axioms off of what "made the most sense" in the real world. Originally one of the axioms of set theory was the axiom of unrestricted comprehension which makes tons of intuitive sense, sadly it turned out it wasn't mathematically valid and had to be replaced with schema of separation which makes very little sense in the real world.

Historically we originally did math off of common sense and intuition. With the belief that the only mathematical systems that were valid were ones that could be represented in reality. Slowly over time formal systems were adopted, and the view switched to the total opposite. Now pure mathematicians develop systems with no care or concern for what exist in the real world, then it's the applied mathematicians job to find a use for them.


What I understand is that if someone makes up their own rules to a mathematical theory they can prove a paradox. I could do that with any form of mathematics. I get the feeling that you're making the subject over complex.

In fact, you've created a paradox by making the statement that 1=.999...

If .999... is a number that cannot exist in the real world but 1 is, then if .999... = 1, then 1 cannot exist in the real world.


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Crowcide

Senior Member

01-24-2013

Quote:
Kaolla:
you're asking me if i know of whatever, and won't tell me why it's relevant. i KNOW it's a red herring so i'm ignoring it

if you wish to persist in this line of inquiry, you can explain it. if not, fine. you can give up

asking if someone knows something in the internet age is dumb, anyone can google what you're talking about. so it's obvious that you have an ulterior motive for trying to get me to acknowledge it.

i don't fall for 1990's message board deceptions

I really doubt your going to be able to google something from an upper division math course that has 4 semesters of calculus as a pre-requisite and understand it.

I'm asking because one of the axioms, the completeness axiom states any LUB of a subset of the reals is also a member of the reals. This is relevant because .999~ being a real number directly follows.

Now, do you understand the axioms of the real numbers?


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Crowcide

Senior Member

01-24-2013

Quote:
Folly Inc:
What I understand is that if someone makes up their own rules to a mathematical theory they can prove a paradox. I could do that with any form of mathematics. I get the feeling that you're making the subject over complex.

In fact, you've created a paradox by making the statement that 1=.999...

If .999... is a number that cannot exist in the real world but 1 is, then if .999... = 1, then 1 cannot exist in the real world.

The rules used to prove .999~ = 1 are ZFC, 1st order logic, and the real axioms. All of which are consistent.

I said .999~ as you describe it isn't in the real world. .999~ as described by math is, as much as any mathematical object exist in the real world.

Any who off to bed for now, will respond tomorrow.