[–]▶ No.33075 [Watch Thread][Show All Posts]
Help me misunderstood genuises! Recently I've been thinking over the 0.999..= 1 argument, as we know
a = 0.(9)
10a = 9.(9)
10a - a = 9.(9) - 0.(9)
9a = 9
a = 1 = 0.(9)
But we can do some fucked up things basing on the simiilar premise:
b = (9)
10b = (9)0
10b - b = (9)0 - (9)
9b = - 9
b = -1 = (9)
c = (9).(9)
10c = (9).(9)
10c - c = (9).(9) - (9).(9)
9c = 0
c = 0 = (9).(9)
a + b = c
0.(9) + (9) = (9).(9)
1 + (-1) = 0
Have I made a mistake somewhere?
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▶ No.33076>>33080 >>33082
b-but it's only equal to one if you round up
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▶ No.33078>>33081 >>33082
There's a pretty big difference between 0.999.. dicks sucked and 1 dick sucked
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▶ No.33080
>>33076
Can you even round up an infinite number?
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▶ No.33081
>>33078
I think 0.999.. dicks sucked is even gayer because that one dick will be sucked forever
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▶ No.33082>>33084
[pop]YouTube embed. Click thumbnail to play.
Made me think of this bit.
>>33076
>>33078
He means 0.999 repeating which is equal to 1. Easiest way of explaining it is this:
1/3 = 0.333 repeating
2/3 = 0.666 repeating
3/3 = 0.999 repeating = 1
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▶ No.33084
>>33082
What if this is just a flaw in base 9(or was it 10?) and we're worrying too much about it?
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▶ No.33086
10a = 9.(9)
this is not correct given the first statement.
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▶ No.33087>>33132
We just equate it to one so it's easy to understand. It's not actually 1, just as .333... isn't truly 1/3rd. Mathfags are pretty autistic about this for some reason. Switch to base 9 if you don't want this problem www.
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▶ No.33132>>33150
Pic related is a formal proof
In my opinion, the easiest way to understand this is:
If .999... wasn't equal 1, then there must exist a number between them, which it doesn't.
>>33087
switching to base 9 just changes the problem to .889.... = 1
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▶ No.33147>>33176 >>33188
>b = (9)
Isn't that only valid for decimals? Even if allowed, common sense dictates that number would just go towards infinity.
However, your bizarre result reminds me of something. Look up the number -1/12, which is supposedly the result of adding all natural numbers together. (Σ=1+2+3+4+5+6+...) Series are weird like that.
Now consider the following.
Your (9) might as well be represented as the following series.
9 + 90 + 900 + 9000 + 90000...
I'm too lazy to work that out but the result being something like -1 isn't as impossible as it seems.
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▶ No.33150>>33157
>>33132
>If .999... wasn't equal 1, then there must exist a number between them, which it doesn't.
but that would mean that:
0.999... + 0.999... = 1.999...998 = 2
and there is indeed a number between that and 2, it's 1.999...
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▶ No.33157
>>33150
1.999...998 is finite not repeating. There would be infinitely many numbers between it and 2, e.g. 1.999...9998 which is also finite. But 1.999... is still equal to 2.
2 = 18/9
1 = 9/9
1.999... = 9/9 + 0.999...
0.999... = 9x
0.999.../9 = 9x/9
0.111... = x
0.111... = 1/9 = x
9x = 9/9 = 0.999...
1.999... = 9/9 + 9/9
1.999... = 18/9 = 2 QED
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▶ No.33176
>>33147
>the number -1/12, which is supposedly the result of adding all natural numbers together.
The "proof" of this is on the level of "proofs" that "prove" 1 = 2.
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▶ No.33188
>>33147
Series are not weird like that, the real series (1 + 2 + …) has no value because it diverges. The -1/12 shit that pops up every now and then is Ramanujan summation, which is something completely different. It only gets brought up all the time because of a Numberphile video that explains it badly in order to make it seem mysterious.
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