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January 16th, 2019, 08:03 AM   #1
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Real numbers and decimals.

All real numbers can be defined by unique decimal sequences unrestricted in length. Convergence in the conventional sense has nothing to do with this.

Addition and multiplication of two endless sequences is a problem because it starts from the right, but there are practical work-arounds which satisfy all the requirements of science and engineering.

If you replace decimal definition with abstract definitions, you regress to people living in caves with rulers who scratch symbols on the walls.

Sequences: Example: 1352976....., .1352976......
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January 16th, 2019, 08:05 AM   #2
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All real numbers can be defined by unique decimal sequences unrestricted in length.
Prove it.
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January 16th, 2019, 08:36 AM   #3
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Prove it.
I said defined by.

What is your definition? Field? Give an example of a member of a field.
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January 16th, 2019, 08:46 AM   #4
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All real numbers can be defined by unique decimal sequences
That's not even true, with infinitely many obvious counterexamples.
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January 16th, 2019, 08:48 AM   #5
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I said defined by.

What is your definition? Field? Give an example of a member of a field.
I agree. You can call things and define them how you want. But if you define things differently from other people, then your proofs do not apply to what other people are talking about.

Your real numbers can be defined by unique decimal sequences unrestricted in length. OK. I have no interest in your real numbers.
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January 16th, 2019, 08:54 AM   #6
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At least show one counterexample if possible.
If not then prove it.

Last edited by idontknow; January 16th, 2019 at 08:58 AM.
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January 16th, 2019, 08:57 AM   #7
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Maschke. Please give "Counter example" {whatever that means}

JeffM1. Please give your definition of a real number and a representative member, other than "x" or "a."

EDIT

I wavered between "represented by" and "defined by". But what is it you are representing? A Dedekind cut? How do you define a Dedekind cut without numbers, and then what decimal do you assign to it?

Last edited by skipjack; January 16th, 2019 at 01:57 PM.
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January 16th, 2019, 10:14 AM   #8
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A representative real number is 1. According to you it has a unique decimal representation. Prove it.

You are the one trying to demonstrate something. I am under no obligation to do anything. I accept that you may define things as you please, but then what you have to say has no relevance to anyone else.
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January 16th, 2019, 10:29 AM   #9
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1 is a real number by definition: it is a unique decimal sequence.

"No relevance to anyone else?" You mean to you, don't you?

Last edited by skipjack; January 16th, 2019 at 01:58 PM.
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January 16th, 2019, 10:42 AM   #10
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Quote:
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1 is a real number by definition: it is a unique decimal sequence.
That is exactly what you must prove, or you are just talking to yourself.
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