Is 1 = 0.999... ? Really?

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Is it true that 1 = 0.999...? And Exactly Why or Why Not?

Yes, 1 = 0.999...
12
32%
No, 1 ≠ 0.999...
22
59%
Other
3
8%
 
Total votes : 37

Re: Is 1 = 0.999... ? Really?

Postby Magnus Anderson » Wed Feb 10, 2021 2:04 pm

wtf wrote:Addition is a binary operation. The only way to define addition of infinitely many summands is to define it as the limit of the sequence of partial sums.


Yes, addition is a binary operation. It is a function that takes two values and outputs a single value. We know that. Do you have anything else to say? Because you are repeating yourself.

You seem to think that an expression such as "2 + 2 + 2" represents an operation of addition that takes three values and outputs a single value. If that's what the expression stands for then it contradicts the definition of the word "addition". As you say, addition takes two inputs; but this expression, you also claim, represents a function that takes three. How can it then be addition? It cannot be -- unless you change the definition of the word "addition" that is. Fortunately for us, that's not what the expression stands for. It stands for a chained series of additions where the result of the first addition (which is "2 + 2") is taken as the input of the second addition. This means that you DO NOT have to redefine the concept of addition. You DO NOT have to extend it so that it can take three (rather than merely two) values as its input.
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Re: Is 1 = 0.999... ? Really?

Postby wtf » Wed Feb 10, 2021 11:11 pm

Magnus Anderson wrote:It stands for a chained series of additions where the result of the first addition (which is "2 + 2") is taken as the input of the second addition.


Exactly what I explained to you in detail a couple of posts back.

Yes you STILL have no definition of an infinite sum, since you can only use induction to reduce a finite sum to a succession of binary operations.

Well folks it's been fun, I'm done here. All the best.
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Re: Is 1 = 0.999... ? Really?

Postby Magnus Anderson » Thu Feb 11, 2021 2:21 am

obsrvr524 wrote:Who said I disagree?

So who would you want to debate?
I can moderate.


I can debate anyone: Certainly Real, phyllo, wtf, Ecmandu, etc. But we'll have to find a set of rules that both me and the other participant are willing to abide by. The job of a moderator (you or anyone else) would be merely to check that the rules are respected and to intercept when violation is suspected.
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Re: Is 1 = 0.999... ? Really?

Postby obsrvr524 » Thu Feb 11, 2021 2:36 am

No one can agree to rules until they hear them. Why don't you propose some on the General Resolution Debate thread. We can talk about it.
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