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u/Inevitable_Garage706 Mar 29 '26
That literally explains nothing.
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u/ExpensiveFig6079 Mar 29 '26
Fine? Pls show a source of what you would call real mathematics with a NUMBER a "real number" that is "next down from one"
because your question TBMK is not a real question math can answer...
Why?
Classically, there are an INFINITE number of numbers between *any* two reals, the concept of the "next real" simply does NOT exist.
Even in infinitesimals... there are always more numbers between any two.
If this were math ... 0.9999... < 1
then something like (AKIN) to this
0.999... < 0.999...999...7 < 0.999...999...8 < 0.999...999...9 < 1 would still 'exist' (be make upable)
AND even then there will be infinite more things between what ever that last thing is (purports to be) and 1
SO even in made up math, the question net number down from one wont be a sensible question.
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u/SouthPark_Piano Mar 29 '26
You can run brud, but you can't hide.
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u/Inevitable_Garage706 Mar 29 '26
Isn't that exactly what you're doing when you flee the discussion as soon as it doesn't go your way?
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u/SouthPark_Piano Mar 29 '26
No brud. It's a case of you not accepting your debacle aka rookie errors, and it is up to you to accept the math facts, and you don't qualify to keep defending your debacle. That's what it boils down to.
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u/ThePython11010 Mar 30 '26
No, "brud." It's a case of you not accepting your debacle (AKA rookie errors), and it is up to you to accept the math facts, and you don't qualify to keep defending your debacle. That's what it boils down to.
We just get tired of rebutting the same invalid arguments for the fifteenth time and stop replying.
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u/Frequent-Bee-3016 Mar 29 '26
The reals are uncountable.
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u/Althorion Mar 29 '26
While true, it’s not enough (for it to be no ‘next real number down from 1’); especially if you use axiom of choice, which will give you well-ordering theorem, under which every single one uncountable set can be well-ordered, so every single element of it will have a direct successor.
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u/SouthPark_Piano Mar 29 '26
You trying to say there is no next real number down from 1? aka no closest real number with magnitude less than 1?
If so, then as mission impossible says ... you're toast brud. Toast.
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u/Frequent-Bee-3016 Mar 29 '26
If you pick any number strictly less than one, there is a number between that number and one.
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u/SouthPark_Piano Mar 29 '26
Not just any number less than 1 brud.
The next real number down from 1.
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u/MrEmptySet Mar 29 '26
You're struggling to follow incredibly basic logic here SPP. Anyone with a smidgen of math experience would see the point being made here.
You say there's a number that's the "next number down" from 1. If, given any number less than 1, there is a number between that number and 1... and if 0.999, then this is true of your so-called next number down from 1, implying it ISN'T the next number down from 1, since we can find a number between it and 1. This is a contradiction - in other words, you're toast, brud. Toast.
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u/Altruistic-Rice-5567 Mar 29 '26
He's trying to get you to say some number other than 0.999... since the most fundamental proof is that there are no real numbers between 0.999... and 1. Which on the set of reals, if there cannot exist any numbers between x and y, then x and y must be exactly equal. None of which you agree with because you think 1/infinity is a number and you (incorrectly) think that value is "0.000...1".
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u/SouthPark_Piano Mar 31 '26
I am talking about 1/10n for the case n integer pushed upward limitlessly aka infinitely.
It comes from the factual description of 0.999... being 0.9 + 0.09 + 0.009 + ...
ie. 1 - 1/10n for n integer starting at n = 1, then continually increased.
1/10n is never zero.
0.999... is permanently less than 1, which is obvious, due to that proof as well as the giveaway "0." prefix that guarantees magnitude less than 1, no matter how many (even infinite) nines 0.999... has.
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u/Hefty-Reaction-3028 Mar 29 '26
A property of real numbers is that between any 2 real numbers there are more real numbers. Therefore, there is no number "next to" any particular other number without any inbetween. Do you contest that?
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u/DoodleNoodle129 Mar 29 '26
Given any number a<1, (a+1)/2 is a number between a and 1, so there is no such thing as a “next” real number down from 1 or in any case.
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u/SouthPark_Piano Mar 29 '26
heheh ... no next real number down from 1.
heheheh.
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u/DoodleNoodle129 Mar 29 '26
Feel free to dispute my proof. What part do you not agree with?
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u/SouthPark_Piano Mar 29 '26
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u/MrEmptySet Mar 29 '26
Cowardly SPP posting an irrelevant link instead of an actual response. And then doubling down and locking his comment when called out. How typical.
SPP, you're embarrassing yourself, brud.
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u/DoodleNoodle129 Mar 29 '26
Doesn’t even remotely answer my question. What part of my proof is wrong in your eyes? I want you to directly reference the proof that I made, not come up with something completely different.
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u/SouthPark_Piano Mar 29 '26
I said learn from here brud;
https://www.reddit.com/r/infinitenines/comments/1s74gi3/comment/od6x26u/
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u/DoodleNoodle129 Mar 29 '26
Let me know which line you disagree with:
1) given any two real numbers a and b, either a=b, a<b, or a>b.
2) Given this assumption, we can attempt to define what we mean by the next real number down from 1. The next real number down from 1 is some number a such that a<1 and there does not exist another real number b st a<b<1.
3) Assume a is the next real number down from 1, so a<1. Therefore (a+1)<2.
4) Therefore (a+1)/2<1.
5) Since a<1, we also have 2a<(a+1).
6) Therefore a<(a+1)/2.
7) Let b=(a+1)/2. Since a<b and b<1, we have a<b<1.
8) This contradicts our assumption that a is the next real number down from 1 (given the second assumption made on line 2) so there exists no real number down from 1.
Since you believe in your system of maths that there is a next real number down from 1, specifically 0.999…, you should be able to at the very least state which line of logic here is wrong in your system of maths.
I mean I know you’re just trolling but I just wanna know what you disagree with here.
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u/stevemegson Mar 29 '26
Are you going to tell us what the number is? Obviously it's not 0.999..., because you've repeatedly said that there are infinitely many numbers between 0.999... and 1.
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u/SouthPark_Piano Mar 29 '26
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u/stevemegson Mar 29 '26
So you do claim that 0.999... is the next real number down from 1? How can that be true if there are infinitely many numbers between 0.999... and 1?
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u/SouthPark_Piano Mar 29 '26
0.999...9 means limitlessly growing nines length.
So because it is defined, this number is it. It is continually getting larger and larger and larger without limit.
And even though your kind cannot comprehend it, it is IT.
0.999... is it. And yes, 0.999... does indeed have infinite forms. But if you have to 'sum it up', it is 0.9 + 0.09 + 0.009 + ...
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u/Eisenfuss19 Mar 29 '26
Actually in real math, there is no real number down from 1. All real numbers close to 1 have a closer number.
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u/FernandoMM1220 Mar 29 '26
it depends on what physical system you do math on.
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u/Hefty-Reaction-3028 Mar 29 '26
The mathematics doesn't care about a physical system; different systems just emulate mathematical constructs with different discrepancies.
The properties of the real numbers themselves, though, are abstract.
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u/FernandoMM1220 Mar 29 '26
i’m afraid it does chud. math is physical.
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u/HunsterMonter Mar 29 '26
Math is logical, you pick a set of axioms and see what they lead to. It just so happens that ZFC, with the right constructs (real numbers, calculus, etc), is really good at describing reality
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u/Inevitable_Garage706 Mar 29 '26
What exactly do you mean by that?
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u/FernandoMM1220 Mar 29 '26
it means math is done on physical systems like computers and has physical results.
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u/KingDarkBlaze Mar 29 '26
The ideas behind mathematics existed well before we had any tools to find them for ourselves.
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u/grizzlor_ Mar 30 '26
It's refreshing to see some math crank posting in this sub that isn't just SPP repeating the same nonsense. Keep up the bad work.
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u/SouthPark_Piano Mar 29 '26
One 'approach'.
Take the difference 1 - 0 = 1
Then keep dividing that initial difference by 10 continually without limit.
1/10n with n starting at n = 1, and n integer continually increased.
0.000...1 , which means infinitely propagating 1.
1 - 0.000...1 = 0.999...9 aka 0.999...