/sci/ - Science & Math

[Anonymous No.15226901]

What would happen if 0.999... did not equal 1.
What would consequences be in other areas of math and outside math?
Would there be any absurd outcomes somewhere else?

[Anonymous No.15226912]

>>15226901
Something like this.
https://en.wikipedia.org/wiki/Hyperreal_number

[Anonymous No.15226937]

>>15226901
The same thing that would happen if you defined 2=/= 6/3

[Anonymous No.15226944]

>>15226937
Wrong and completely braindead take.

[Anonymous No.15226948]

>>15226901
it doesn't

[Anonymous No.15226967]

>>15226901
this thread again

[Anonymous No.15226984]

>>15226944
Two different ways of writing the same number in both cases

[Anonymous No.15227074]

>>15226948
We're not having that debate today

[Anonymous No.15227075]

>>15226984
You truly are braindead. OP is specifically asking about the implications of the two not being the same number.

[Anonymous No.15227168]

The Heisenberg Uncertainty Principle would break down, so you could know a particles position and momentum to arbitrary precision: https://terrytao.wordpress.com/2007/07/27/dyadic-models/

[Anonymous No.15227189]

>>15226901
?

x = 0.999...
10x = 9.999...
10x - x = 9
9x = 9
x = 1

=> 0.999... = 1

[Anonymous No.15227191]

>>15227168

[Anonymous No.15227192]

>>15227189
You need to be 18+ to post here.

[Anonymous No.15227218]

>>15227189
That's the wrong proof
https://www.youtube.com/watch?v=wsOXvQn3JuE

[Anonymous No.15227225]

>>15227218
>taking 3 minutes to say that 0.999... needs to have a defined real value in the first place before you can do algebra with it and claim it's rigorous.

[Anonymous No.15227232]

>>15226901
Nothing, you can already do this today. You can define the real numbers as Cauchy sequences, period. No quotient at all. You'll get something basically unusable, but you can probably design some random algebraic equations for it out of your arse.

[Anonymous No.15227478]

>>15227075
And I told you what the implications would be, the same as any other 2 numbers that are the same not being the same anymore.

[Anonymous No.15227716]

>>15226901
I'm assuming you want the numbers to still be an ordered field, but are willing to drop the Archimedean property so that 0.999... can be infinitesimally less than 1. You would need extra structure (e.g. surreal numbers' "simplicity" or the idea of a "standard real number" from the hyperreals) to make infinite decimals define a unique number, since the old definitions would no longer suffice. Having done this, you would find there would be numbers that cannot be written as an infinite decimal. Also many proofs involving calculus, such as the formula for the area of the circle, would fall through unless you added additional assumptions (e.g. the hyperreal numbers' transfer principle).

For applied stuff it would not matter because you can just ignore infinitesimal differences between numbers, which gives you back the old real numbers. Whether there are infinitesimal distances, times, masses, etc. in the physical universe we do not know and may not be able to find out.

[Anonymous No.15227745]

>Ladies and Gentlemen,
>May I have your attention, please.
>I have invented a most marvelous device
>With this device, I can make 0.9999 repeating not equal 1
>All I have to do is turn this switch on
>And after I have turned it off
>0.9999 repeating equals 1 again

[Anonymous No.15227760]

>>15227478
Yes, but you are wrong and delusional, because there is no specific reason why it should have such implications.

[Anonymous No.15227811]

>>15227745
Nice! Great that minds of /sci/ finally reached current science in the year 23. 1823.

[Anonymous No.15227836]

>>15227192
I'm older than you dumbass

[Anonymous No.15227837]

>>15227225
Yes.

[Anonymous No.15227841]

>>15227760
what implications? I never listed any.

[Anonymous No.15227867]

>>15227841
Have you taken your medications today? In any case, one possible way it won't equal 1 is if the sequence 0.9, 0.99, 0.999, ... is indexed by hyperintegers, which gives you infinitely many hyperreals infinitely close to 1 but not equal to it.

[Anonymous No.15227887]

>>15227867
cope and seethe, I already won

[Anonymous No.15228675]

>>15227716
Thanks. I'm thinking 0.999 isn't equal 1 because there's no consequences

[Anonymous No.15228951]

>>15226901
You'd be rounding down instead of up? At best you might change cryptography that doesn't distinguish on that arbitrary approximation. Absurds over selling the change.

[Anonymous No.15230672]

>>15226901
In the system of reals we can prove from axioms that 0.999... = 1
If we use different axioms, like >>15226912
suggests, then we can make sense of a statement somewhat like 0.999... != 1 by replacing it with 1-ε != 1 where ε is "infinitely small".

[Anonymous No.15230695]

Then I would be able to divide any number by (1-0.9...).

[Anonymous No.15230700]

>>15230695
or 0.9... - 1

[Anonymous No.15230857]

>>15226901
0.999... isn't an actual number
Just an alternative way to write 1
It's like saying "what'd happen if 1≠1?"

[Anonymous No.15232573]

0.999...98

[Anonymous No.15232667]

but 1+1=2 is wrong because 1 is always diferent from 1 and there are no 2 identical things in the world this is why 1+1=1,99999999999

[Anonymous No.15232767]

>>15226901

If two numbers are NOT equal then there is space on the number line between them and thus there IS a number halfway between them.

If 0.9999... is NOT equal to 1 then please define the number between them!!!

[Anonymous No.15232791]

>>15232767
.9... equals .9...8
and .9...8 != 0
therefore .9... != 0

[Anonymous No.15232807]

>>15232791
>.9... equals .9...8

WTF is 9...8
There is no way to express a continuation after an infinite sequence. Where is the LAST 9 in 0.999... for you to add an 8 afterward???

[Anonymous No.15232853]

>>15232807
1 - .9... = .0...1
.9... - .0...1 = .9...8
.9...8 - .0...1 = .9...7
.9...7 + 3 * (1 - .9...) = 1

[Anonymous No.15232857]

>>15232767
>If 0.9999... is NOT equal to 1 then please define the number between them!!!
All numbers of the form 1-epsilon for some infinitesimal epsilon.

[Anonymous No.15232877]

>>15226901
ITT: people argue about algebro-geometric concepts while trying not to use any algebraic geometry

[Anonymous No.15232898]

>>15226901
If 0.999... is distinct from 1, then what is the number that is in between them? And can you write it down? (This is left as an exercise to the reader).

[Anonymous No.15233342]

>15227218
>https://www.youtube.com/watch?v=wsOXvQn3JuE
> Saying that .999... = x implies 9.999... =10x is like saying that .222... = x implies that 2.222... = 2x
What? Does she even understand that in the proof it was just multiplying by 10?

[Anonymous No.15233361]

>>15226901
dense ordering of reals would become fuddlore, which it already should

[Anonymous No.15233630]

>>15232877
To expand on this: see
https://ncatlab.org/nlab/show/infinitesimal+object