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March 31st, 2019, 08:53 AM   #21
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Quote:
Originally Posted by zylo View Post
To count the real numbers in [.1,1), remove the decimal point.
It doesn't help your argument when you don't express, them well; but it also doesn't help those pointing out how wrong you are to ignore the obvious corrections, tempting as it is:
"To create a bijection between the natural numbers, N, and the real numbers in range [.1,1), R1, remove the radix point from the decimal representation of each member of R1 and assign the natural number represented by this new string to that real number."
If this is what you meant, then you clearly have no understanding of what you think you are talking about.

Quote:
Originally Posted by zylo View Post
[.1,1) is an interval of real numbers.

.1 -> 1
.105 -> 105
.13 -> 13
.333 -> 333

Every real number in the INTERVAL [.1,1) maps to a unique natural number.
Since 0.105, 0.0105, 0.00105, ..., all map to 105, you are wrong. They are not unique.

Quote:
I'm trying to make it as simple as possible.
No, you are trying to get other people to agree to what you want to be true, but that has repeatedly been shown to not be true.

Quote:
Originally Posted by Phrzby Phil View Post
Your example of four numbers above conveniently does not include any reals with an infinite number of (non-zero trailing) digits.
This is another point zylo ignores. When you remove the decimal point from the representation of 1/3, which is "0.333...", you get something that cannot be the decimal representation of a natural number.

+++++

In short, it is even less helpful when it is easier to see why your "simple" demonstrations are wrong, than when they are just poorly expressed.
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March 31st, 2019, 10:24 AM   #22
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Quote:
Originally Posted by JeffJo View Post
Since 0.105, 0.0105, 0.00105, ..., all map to 105, you are wrong. They are not unique.
As 0.0105, 0.00105, etc., aren't in [0.1, 1), that objection doesn't work.

Quote:
Originally Posted by JeffJo View Post
This is another point zylo ignores. When you remove the decimal point from the representation of 1/3, which is "0.333...", you get something that cannot be the decimal representation of a natural number.
Not a natural number as usually defined, but zylo has previously relied on his own definition of natural numbers and ignored objections that his own definition renders them uncountable.
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