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That would make it a rational number, so we can rule that out


Exactly, the only possible "last digit" it could have (in keeping with the silly premise that it has one), is zero.


The only possible "last digit" it could not have is zero: if the last digit were to be a zero, that digit would be superfluous and could be discarded, making the digit before that the real "last digit".

Proof: the first digit of pi is 3, not zero.


sigh It was said in jest, in response to another comment also said in jest.

That aside, the apparent "empty space" on the either side of a number is in reality consisting of infinite zeroes.

Just because we typically choose to "display" most numbers without those zeroes, it doesn't mean they aren't there in a very real, practical and important sense.

They are there, because if they aren't there, then something else might be, and then all our numbers would have to be assumed to be wrong or incomplete... so instead, we assume the zeroes.

The terrible reality is the zeroes extend off infinitely in either direction, and we use empty space as shorthand for this so we don't have to spend longer than the age of the universe to write a single number with full accuracy.


I don't think that would be true seeing 1/3 = 0.3333.. , or am I reading this wrong?


3 recurring represents a particular quantity continuing forever.

0 recurring represents the end of a quantity, and the absence of any further quantity, forever.

Eg: 0.012500000000000...

The significant portion is 0.0125 - the recurring zeroes serve a mathematical role akin to that of a full-stop in a sentence. Hence zero being (jokingly, but in a sense truthfully) always the "last digit".


This is just an artifact of representing it in base-10. In base-3 0.0125 has the same value but would have a non-terminating representation of 0.00010001...

I will grant that in base-π, π is 10, however.


Why is zero different than any other number?


It acts as a terminator or terminal, see https://news.ycombinator.com/item?id=34391483.


If 0 would act as a terminator, then 1.203 would be equal to 1.2.

The thing that is actually special about the digit 0 is that it is implied for all positions for which no digit is given. That is, when we write

          1.2
we really mean

  …00000001.20000000…




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