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Topic: 1/3/2018 : If you claim 0.999... is a rational number, then you
must find p/q such that 0.999... = p/q.

Replies: 2   Last Post: Jan 4, 2018 4:47 AM

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zelos.malum@gmail.com

Posts: 1,176
Registered: 9/18/17
Re: 1/3/2018 : If you claim 0.999... is a rational number, then you
must find p/q such that 0.999... = p/q.

Posted: Jan 4, 2018 2:50 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

To understand decimals you need to understand that when we write N.abcdefg.... we are refering to a function f:Z x {0,1,2,3,4,5,6,7,8,9}^N -> R defined as

f(n,(b_i))=lim(m->oo) n+sum(i<=m) b_i

as such we have 0.111... = lim(n->oo) 1/10^n

and it works as it should. You are just too stupid to understand.

And no, there is not 3 rules, there is just one definition. Learn it.

That is like saying there are 3 cases of second degree equations, but that is because you can technically dividei t up if you only care about real solutions but in reality, there is just one.



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