Here is a classic exercise: Which of the following are true and why?

0.99999..... < 1

0.99999..... = 1

0.99999..... > 1

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Guest Message by DevFuse

Started by BMAD, Oct 20 2013 12:32 AM

11 replies to this topic

Posted 20 October 2013 - 12:32 AM

Here is a classic exercise: Which of the following are true and why?

0.99999..... < 1

0.99999..... = 1

0.99999..... > 1

Posted 20 October 2013 - 03:24 AM Best Answer

Spoiler for

Posted 20 October 2013 - 11:00 AM

Spoiler for Simplest proof

- Bertrand Russell

Posted 20 October 2013 - 02:16 PM

So are we saying only one case is true?

Posted 20 October 2013 - 04:28 PM

So are we saying only one case is true?

Yes. Both sides of the relations specify real numbers, which are well-ordered. So, exactly one of the relations must be true.

Posted 04 November 2013 - 05:31 PM

hmm. there's a mathematician on youtube, norm wildberger, whom i kinda like who would disagree.

the problem being that we cant actually "know" infinity. try writing infinite 9's. you can't.

so at best we can say 0.9999999 or wherever you care to stop approximately equals 1.

to prove this point, accurately calculate pi +e +sqrt(2). if you're being honest, you would calculate it as pi + e +sqrt(2).

Posted 04 November 2013 - 06:06 PM

Spoiler for a simple proof

Past prime, actually.

Posted 05 November 2013 - 03:12 PM

hmm. there's a mathematician on youtube, norm wildberger, whom i kinda like who would disagree.

the problem being that we cant actually "know" infinity. try writing infinite 9's. you can't.

so at best we can say 0.9999999 or wherever you care to stop approximately equals 1.

to prove this point, accurately calculate pi +e +sqrt(2). if you're being honest, you would calculate it as pi + e +sqrt(2).

The notation convention 0.999 ...

You can't

Thus, given the meaning of that notation, one can meaningfully write 1/3 = 0.333 ...

Similarly one can meaningfully write 1 = 0.999 ...

- Bertrand Russell

Posted 05 November 2013 - 06:38 PM

well, not entirely sure i agree. for example, how would you denote 1/13?

you need a consistent way of denoting any rational number, not just ones that repeat the last digit.

personally, i like the bar method, where the repeated values have a bar over the top over the length of the repeating part.

so

_ 0.9 = 1

would be more accurate (although more cumbersome.)

Posted 05 November 2013 - 07:00 PM

here's my challenge for you.

accurately add 1/13 to 45/89 in decimal representation.

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