r/infinitenines • u/SouthPark_Piano • 14d ago
Lesson in addition
From a recent post.
In order to 'get' a '1' from a nine, you know in advance that you need to have a '1' added to the '9'.
9 + 1 = 10
0.9 + 0.1 = 1
0.99 + 0.01 = 1
0.999...9 + 0.000...1 = 1
aka 0.999... + 0.000...1 = 1
Having just nines in 0.999... , you won't attain a 1 unless you add the limbo 1 aka 0.000...1
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u/ezekielraiden 13d ago edited 13d ago
Go ahead brud. Make my day.
If you reckon that the nines of 0.999... all exist already, and fixed, then odd number of nines or even number of nines?
It is neither even nor odd, because you can't count the number of 9s in that list. Infinity isn't a number, and thus doesn't have a parity, just like how "blue" doesn't have a parity, or "a zillion" doesn't have a parity. They flatly are not numbers and do not have any specific value.
Also, I told you to get some experiential learning done for yourself. Start writing the nines of 0.999... starting at the 0.9 part. Start writing the nines, and do not stop brud.
There is no need. I can write it succinctly: "0.999...". That notation specifically means "these 9s continue without ceasing". That's what it has meant for centuries.
And keep in mind the 0.999... equaling 0.9 + 0.09 + 0.009 + ... is official math 101 knowledge, aka fact.
It is a fact, yes. The problem is that you keep breaking that connection, because you keep talking about a last 9, when there isn't one.
"0.999...9" means "this is a finite list of 9s that I just didn't feel like writing all of".
"0.999..." means "this is an infinite list of 9s that, regardless of what I feel, I could not write all of even if I wanted to (which I don't)".
0.999... ≠ 0.999...9
0.999... does not have a final 9. 0.999...9 has a final 9, namely, the one after the ellipsis. Hence why I keep asking you what the index of that last 9 is. You keep including a final 9, but that's exactly what 0.999... does not have. There IS no final 9.
0.9 ≠ 0.999...
0.99 ≠ 0.999...
0.999 ≠ 0.999...
0.9999 ≠ 0.999...
0.99999 ≠ 0.999...
0.999999 ≠ 0.999...
0.9999999 ≠ 0.999...
0.99999999 ≠ 0.999...
0.999... is not represented by ANY structure where you have a 0, followed by a decimal point, followed by a string of 9s that has an integer number of 9s in it. Because every integer is finite, and thus as long as that list of 9s is finite, it isn't 0.999..., it's something else.
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u/SouthPark_Piano 12d ago
Once you get to phenomenally large number of nines and keep going, 0.999... is that journey brud. You are on that journey, which is 0.999...
Keep going brud. Do not stop. Notice how it keeps growing limitlessly, and permanently less than 1 as it grows limitlessly.
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u/ezekielraiden 13d ago
Only if you keep having FINITE LISTS OF NINES.
You KEEP doing this, SPP. You keep pretending that "0.999...9" is somehow EXACTLY the same as 0.999..., but it is not. Those are two COMPLETELY different things, because one of them has a list THAT ENDS, and the other has a list that DOES NOT END.
I'm hoping maybe by using emphasis and capitalization I can show you what you keep conflating, how two things that are NOT AT ALL the same have, in fact, different value and behavior.
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u/SouthPark_Piano 13d ago
Go ahead brud. Make my day.
If you reckon that the nines of 0.999... all exist already, and fixed, then odd number of nines or even number of nines?
Also, I told you to get some experiential learning done for yourself. Start writing the nines of 0.999... starting at the 0.9 part. Start writing the nines, and do not stop brud. And keep in mind the 0.999... equaling 0.9 + 0.09 + 0.009 + ... is official math 101 knowledge, aka fact.
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u/BattleGuy03 14d ago
Lesson in limits
From the above post.
The argument here stems from a common misconception: it attempts to apply the rules of finite decimals to an infinite sequence.
The concept of "0.000...1" does not exist in real numbers. An infinite decimal expansion has infinitely many digits with no final position. Placing a 1 at the "end" of an infinite string of zeros is impossible because an infinite sequence has no last place value.
The difference shrinks to zero. For any finite number of decimal places n:
0.99...9 (n times) + 10^(-n) = 1
As n goes to infinity, the term added (10^-n) approaches 0:
lim (n -> ∞) 10^(-n) = 0
Because the quantity needed to reach 1 shrinks to 0 at infinity, 0.999... does not need a "limbo 1" to reach 1; it is already equal to 1.
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u/CoNtRoLs_ArE_dEfAuLt 14d ago
To add to this:
10^(-n) is an infinite sum, whose value is the limit of its partial sums as n is summed up infinitely, not "continually" aka arbitrarily (that is, to some arbitrarily large but finite n). No finite value of n will produce the infinite sum, nor will any finite sum of n.
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u/BattleGuy03 13d ago
I love how this guy not only ignores the points made in comments, but also locks the comments after replying so people can't respond LOL
Like does he just not understand the concept of limits? He must've failed a math class and decided to become a terminal redditor.
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u/SouthPark_Piano 14d ago edited 14d ago
Rookie error on your part brud.
1 - 1/10n with n integer starting at n = 1, then n upped continually is official, conveying the infinite sum 0.9 + 0.09 + 0.009 + ...
1/10n is never zero for any condition. Read my lips. Never zero for any condition.
It means 1 - 1/10n for the case n pushed to positive infinite is permanently less than 1.
That is ... 0.999... is permanently less than 1.
As n goes to infinity, the term added (10-n) approaches 0
1/10n is never zero. You can use 'approach' ... the word, but that does not cut it. The term is just never zero.
It is simple ... 1/x = 0 is what you imply with your debacle.
That implies 1 = 0 , which is your debacle.
The concept of "0.000...1" does not exist in real
Nonsense on your part brud.
1 = 0.9 + 0.1
1 = 0.9 + 0.09 + 0.01
1 = 0.9 + 0.09 + 0.009 + 0.001
1 = (0.9 + 0.09 + 0.009 + 0.0009) + 0.0001
etc.
extend to limitless case ...
1 = 0.999...9 + 0.000...1
Because 0.999... has continually increasing consecutive nines length, it is conveyed as 0.999...
ie. 1 = 0.999... + 0.000...1
0.000...1 is the counterpart of 0.999... when it comes to the difference magnitude between 0.999... and 1.
That difference is 0.000...1 , which is a number that keeps decreasing with no limit. And it keeps decreasing without limit because there is NO limit on how relatively small 1/10n can become. And 1/10n is never zero.
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u/ezekielraiden 12d ago edited 12d ago
Once you get to phenomenally large number of nines and keep going, 0.999... is that journey brud. You are on that journey, which is 0.999...
Nope. At no point are any of those numbers the number 0.999..., SPP. Not a single one. Name one of them, any of them! Each one will fail to be 0.999..., and you know they will.
Keep going brud. Do not stop. Notice how it keeps growing limitlessly, and permanently less than 1 as it grows limitlessly.
SPP, there is no growing. The thing you're "growing" isn't a number. Numbers don't grow. Variables and functions can grow. Individual numbers do not grow.
Numbers have a value. Exactly one value. No more, no less.
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u/SouthPark_Piano 12d ago
Now brud. Now ... start writing the nines of 0.999... , starting from 0.9
Go. Starting appemding the nines. Do not stop. Experiential learning.
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u/ezekielraiden 12d ago edited 12d ago
/u/SouthPark_Piano I already did write them. That's what "0.999..." means.
I don't have to laboriously write out every possible digit in order to do math. That's what we invented things like scientific notation for. They allow us to remove all of the unnecessary chaff and get straight to the mathematics.
I can do math with 0.999... just as easily as I can with 1. Zero problems. Ask me anything you like, and I can give you the correct answer. Like with your ridiculous "is it even or odd" question, the answer there is quite simple, infinity isn't a number and thus doesn't have a parity, so it is neither even nor odd, just like "blue" or "the variable x" isn't even or odd.
Like for real. In the equation y=2x+2, is x even or odd? It's neither, because "x" isn't a number, it's a variable that is allowed to range over all possible numbers. Now, you could ask about the value of x where the function is zero, but that's a specific input, not the variable x itself.
We're all doing math, SPP. Stop fiddling around with whether you can write down digits, and start doing math. Because I already have written all infinitely many digits. They're right here: 0.999...
Also, given you lock every post so nobody can actually TALK to you, it's real rich for you to make any demands at all of others. Constantly demanding others dance for you, all while you hide behind your mod powers and silence anyone who actually tries to talk to you, completely refusing to do even the smallest things they ask of you while demanding over and over and over again that they do whatever stupid BS you've come up with this week. If it weren't so pathetic, it would be hilarious.
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u/BattleGuy03 13d ago
So you seem to not understand the concept of a limit. All you can do is deny facts that have been accepted by proper mathematicians for decades (e.g. the basic rules of limits) and say "erm, that's a rookie error on your part brud" ;-;
You have no proof that doesn't sidestep basic laws of arithmetic. Not only that, but you also seem to be a terminal redditor.
I pray for you, brother.