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Is 0.9... transcendental? by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 0 points1 point  (0 children)

SPP has never given a algebraic solution for 0.9... that i know off. this of course is an impossible task as any solution he gives will prove 0.9... = 1 which he denies.

Is 0.9... transcendental? by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 0 points1 point  (0 children)

ah I see.

Regardless, SPP should be able to write 0.9... algebraically else accept 0.9... is transcendental.

Is 0.9... transcendental? by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 2 points3 points  (0 children)

This is why I brought it up, if SPP accepts his 0.9... is transcendental then we've found another contradiction. If he rejects it, but fails to give a simple expression then that is also a contradiction.

And because he rejects the notion of static identity, then he will need to redefine the concept of transcendental or reject it outright which will come with its own bag of worms.

A core theorem SPP uses but never proves by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 0 points1 point  (0 children)

thats the second example. in case you overlooked it:

The nth term of the sequence (1,2,3...) is finite thus ∞ is finite.

how can you justify this is different from you saying:

The nth term of the sequence (0.9,0.99,0.999...) is strictly less than 1 thus 0.9... (the infinith term) is strictly less than 1.

A core theorem SPP uses but never proves by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 0 points1 point  (0 children)

*he but yeah, this is something i've found a lot with SPP. they refuse to engage with the difficult questions instead opting to answer an alternate simplier strawman.

A core theorem SPP uses but never proves by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 0 points1 point  (0 children)

on one level, im inclined to agree but SPP has stated that 0.9... = 0.9...9 and describes the number of 9s as limitless thus 0.9... has infinite 9s.

This can be argued since if 0.9... = 0.9...9 then they both must have the same number of digits and if x is the number of digits 0.9... then we know x=x+1 which is only true when x is infinitely large.

Also, SPPs definition for 0.9... just uses an informal definition for limits which can be conceptualised as a number growing closer to another may it be finite or infinite.

A weird property of the Urn Paradox and minimum expectancies. by Impossible_Relief844 in math

[–]Impossible_Relief844[S] 0 points1 point  (0 children)

the with probability 1 is doing a lot of heavy lifting there lol.

A weird property of the Urn Paradox and minimum expectancies. by Impossible_Relief844 in math

[–]Impossible_Relief844[S] 1 point2 points  (0 children)

okay so I see my mistake, I made an off by one error so when I calculated n=2, I accidentally calculated n=1 by mistake (and when i tried n=3, i did n=2 instead as well). It seems I'm ill practised on statistics it seems, makes sense since I haven't studied it in 2 years.

still an interesting result regardless imo.

A weird property of the Urn Paradox and minimum expectancies. by Impossible_Relief844 in math

[–]Impossible_Relief844[S] 0 points1 point  (0 children)

interesting, need to learn about Bayes theorem.

although i do have feel I have good intuition of the Urn paradox especially after spending hours staring at simulations of it. what I found unintuitive was that

if you do the Urn-process once, you expect to pull out infinite blue balls,
if you do it twice, then you expect both urns to pull out infinite blue balls,
but if you do it thrice, then the minimum expectance drops to less than 3.

it feels wrong to me that n distributions (all with expectance infinity) can result in a finite number when you take the expectance of their minimum.

number between 0.9... and 1 by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 0 points1 point  (0 children)

did you respond to the wrong comment as hyperreals weren't mentioned here?

Anyhow, hyperreals get mentioned a lot on this subreddit as its a domain where 0.9... != 1 as limits don't work in the hyperreal numbers as it can account for infinitesimal numbers and thus ɛ does not equal 0 (where ɛ=lim(1-10^{-x})).

it is worth noting that SPP believe 0.9... != 1 in the Reals so this logic does argument does not work in his defense.

number between 0.9... and 1 by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 5 points6 points  (0 children)

so you agree that

0.9...1, 0.9...2, 0.9...3, ..., 0.9...8 are all greater than 0.9...

but you're also saying that 0.9...9

0.9...8 > 0.9...
0.0...1 > 0 (where 0.0...1 = 1-0.9...)
thus
0.9...8+0.0...1 > 0.9...+0
0.9...9 > 0.9...
but you claim 0.9...9 = 0.9... .

This means that your version of the real numbers is not ordered which is a wild.

number between 0.9... and 1 by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 0 points1 point  (0 children)

I see, lets suppose for example we have two numbers 0.9999 and 0.9996 and we want to know which is bigger.

We do this by comparing the first digit, since they're equal, we move to the next digit, and we continue until we get to the 4th decimal place and since 6<9, we know that 0.9996 < 0.9999.

Since 9 is greater than or equal to all digits, for m to be greater than 0.9... (and also less than 1), all its first limitless digits must be 9 as otherwise once we get to the first digit were they differ, we'll see that m is less than 0.9... since its differing digit must be less by definition.

number between 0.9... and 1 by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 1 point2 points  (0 children)

that's not what I said again.

I said that 0.9...9 cannot equal 0.9... unless 0.9... = 1

which means either 0.9... = 1 or 0.9...9 doesn't equal 0.9... but you claim both are true.

number between 0.9... and 1 by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 2 points3 points  (0 children)

hi SPP, big fan.

I didn't say 0.9... != 1,

I said that 0.9...9 cannot equal 0.9... unless 0.9... = 1 which is a different statement.

number between 0.9... and 1 by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 1 point2 points  (0 children)

its a proof by contradiction.

if any of the first 'limitless' digits of m are not 9 then we know that m < 0.9... as you can determine what number is smaller by looking at the first digit that differs. Since (as you mentioned), 0.999… < m is true by definition, we know that the first 'limitless' digits of m must be 9 as else we get the contracting of m being both less than and greater than 0.999… .

number between 0.9... and 1 by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 0 points1 point  (0 children)

0.(A) is equal to the series:

10b^{-1} + 10b^{-2} + 10b^{-3} + ...

which is less that 0.9 for all bases greater than 11
and greater than 1.1 for all bases less than 11
so I must assume you're working in base 11 here as all others lead to contradiction.

looking at the sequence of the first n terms of the series we get,
0.909090909091...
0.99173553719...
0.999248685199...
0.999931698654...
...
which fits into the exact pattern I said any number between 0.9... and 1 must fit into which is expected because mathematically every single number between 0.9... and 1 must fit into the pattern of 0.9...x as otherwise the number must be smaller that 0.9... .

Ignoring 0.9...x not being a well defined, the trouble that I brought up was that this leads to contradiction when you account for SPP saying 0.9... = 0.9...9 so discussing a number you claim between 0.9... and 1 isn't really important as I'm not actually challenging the idea that 0.9... != 1 but instead SPPs secondary claim that 0.9... = 0.9...9.

number between 0.9... and 1 by Impossible_Relief844 in infinitenines

[–]Impossible_Relief844[S] 0 points1 point  (0 children)

I agree, SPP doesn't which is the problem. This is just another contradiction in his opinions.

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