/sci/ - Science & Math

[EconPoser !nHKvW0t1cI No.4622632]

If <span class="math">0.\bar{9} \not = 1[/spoiler] then the set of real numbers cannot be constructed from Dedekind cuts. Discuss.

[yeep !HCCDB7tu.A No.4622636]

but it does, so what is there to discuss? haha

[IQ fundie !!8XTTCUzK2no No.4622637]

Nothing to discuss. You made a claim, OP, so it's up to you to prove it.

[EconPoser !nHKvW0t1cI No.4622649]

>>4622637
>>4622636

Just saying, since people always throw a hissyfit about <span class="math">0.\bar{9} \not = 1[/spoiler] but never gave a damn about real numbers. Construction is very similar, after all.

[Anonymous No.4622658]

[IQ fundie !!8XTTCUzK2no No.4622660]

>>4622649
Irrelevant. You made a statement and that statement cannot be considered true unless you prove it.

[IQ fundie !!8XTTCUzK2no No.4622664]

>>4622658
>a simple proof by induction
That's wrong. The proof doesn't use induction.

[Scientist !!ThFjnJh4EkH No.4623796]

>>4622632
But the Real Numbers are constructed by Dedekind cuts, and thus your assertion is nonsensical.

[Anonymous No.4623804]

>>4623796
they can be constructed from cauchy sequences in Q also

[Scientist !!ThFjnJh4EkH No.4623805]

>>4623804
And it's provable that they're equivalent.

[Anonymous No.4623812]

>>4623805
Prove proofs prove proofs.

[Anonymous No.4623813]

>>4623805
yes, obviously

so if you start with 0.999... =/= 1 then you have a cauchy sequence that isn't identified with it's limit (all in Q), breaking the whole construction

[Anonymous No.4624074]

>If A = B then there would be odd repercussions

Wowzers, what a thread.

1/3 = 3.33333~
1/3 + 1/3 + 1/3 = 0.99999~ = 3/3 = 1