The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Replies: 5   Last Post: Oct 4, 2017 3:15 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 5,511
Registered: 9/25/16
Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Posted: Oct 3, 2017 5:33 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Why are they the same? Simply because oo is not
an element from the natural numbers. So

\sum_{k=1}^oo 9/(10^k)

cannot mean something where the last summand is
9/(10^oo) because a value 9/(10^oo) doesn't exist

in Q, since there is no k=oo. So all you have is
the partial sums that go on and on,

\sum_{k=1}^n 9/(10^k)

And you cannot identify a final value. To extract
a value from the series you need the limes.

Am Dienstag, 3. Oktober 2017 23:21:40 UTC+2 schrieb
> Since \sum_{k=1}^n 9/(10^k) = 1 - 10^(-n),
> and \sum_{k=1}^oo a(k) = lim n->oo \sum_{k=1}^n a(k)
> The two are synonymous:
> lim n->oo (1-10^(-n)) = \sum_{k=1}^{\infty} 9/(10^k)
> BTW: The following authors here on sci.math already
> explained this two you like a dozen times:
> - Dan
> - Me
> - Markus Klyver
> - Zelos Malum
> - Etc..
> You, bird brain John Gabriel, probably qualify
> for the most stupid human being on the planet.
> Should we call the Guiness book of records?
> Am Dienstag, 3. Oktober 2017 22:04:52 UTC+2 schrieb John Gabriel:

> > > lim n->oo (1-10^(-n))
> >
> > No. 0.999... = \sum_{k=1}^{\infty} 9/(10^k)

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.