Re: Does the number of nines increase?

On 04/07/2024 21:01, FromTheRafters wrote:

Chris M. Thomasson laid this down on his screen :

On 7/4/2024 9:58 AM, FromTheRafters wrote:

Peter Fairbrother formulated on Thursday :

On 25/06/2024 21:18, WM wrote:

Let the infinite sequence 0.999... be multiplied by 10. Does the number of nines grow?
Corollary-question: Does the number of nines grow when in 0.999 the decimal point is shifted by one or more position?
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Regards, WM

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A more interesting question; suppose a set containing an infinite number of 9's. Now copy that set and add a 2.
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Is the second set bigger than the first set?
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Peter Fairbrother

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Lrf, pneqvanyvgl bar naq pneqvanyvgl gjb.

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Different set with an infinite number of elements. Their sizes are the same for infinity = infinity... :^)

 Providing one infinite set and the other are both countable or both uncountable. If one set is size Aleph_zero and the other is 2^Aleph_zero then they are not the same size.

I imagined the 9's as being the last digits of 0.99... so distinguishable and countably infinite.
But the second set is also countable.
So the sets have the same cardinality, (?and the same size?), but the element 2 is in one set but not in the other, and no other element is in one set but not the other.
Peter Fairbrother