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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

 Messages: [ Previous | Next ]
 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

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.