Math Is Fun Forum

Jeremy Desmond

Member

Registered: 2022-08-22

Posts: 13

Splitting hairs?

Hello,

I would be grateful if someone could explain to me the following please.

Since 1/9 = 0.11111….., does 9/9 = 0.99999….. or 1 exactly?

What is the difference between 0.9 recurring and 1.0 recurring?

I can’t get my head round this. At first glance it seems like a loophole in strict Aristotelian logic.

Thanks.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,182

Re: Splitting hairs?

Hi,

Please see the link: The idea is that 0.9 recurring (0.999... with the digits going on forever) is actually equal to 1.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jeremy Desmond

Member

Registered: 2022-08-22

Posts: 13

Re: Splitting hairs?

Thank you ganesh,

I think I understand what it says on that ‘Maths Is Fun’ page. At least, I understand the logic of it. But I still don’t find it satisfactory. Have you or has anyone else got any philosophical comments about this phenomenon? It implies that 0.000…0001 is equal to zero, which doesn’t feel correct.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,182

Re: Splitting hairs?

Hi Jeremy Desmond,

Please see the mathematical reasoning:

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.