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0 pointskazinator9y ago0 comments

> find a decimal representation of a number

0.99999999...1

This denotes the abstract idea that we take 0.999... (infinite number of 9's) and add another digit.

This is no more or less abstract than 0.999... to begin with.

0.999... is a unicorn, and 0.999...9 is a unicorn with a pink ribbon on the tip of its horn.

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lisper9y ago

> add another digit

But you can't. All of the places where you might want to add a digit are already occupied by 9's.

kazinatorOP9y ago

So you're saying a countable infinity can be occupied, so that there is no room for one more.

You must then disbelieve concepts such as that the even integers can be put in 1:1 correspondence with all integers; i.e. that there are exactly as many even integers as there are integers.

lisper9y ago

> So you're saying a countable infinity can be occupied, so that there is no room for one more.

No. I'm saying that a countable infinity doesn't have room for one more at the end. There is no end.

You can obviously stick a 1 in the middle, but then you have a number strictly less than 0.999...

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lisper9y ago

> add another digit

But you can't. All of the places where you might want to add a digit are already occupied by 9's.

kazinatorOP9y ago

So you're saying a countable infinity can be occupied, so that there is no room for one more.

You must then disbelieve concepts such as that the even integers can be put in 1:1 correspondence with all integers; i.e. that there are exactly as many even integers as there are integers.

lisper9y ago

> So you're saying a countable infinity can be occupied, so that there is no room for one more.

No. I'm saying that a countable infinity doesn't have room for one more at the end. There is no end.

You can obviously stick a 1 in the middle, but then you have a number strictly less than 0.999...

2 more replies

j / k navigate · click thread line to collapse