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I asked a friend
>If there is an infinitely long number comprised entirely of 1's and 0's, are there an infinite number of both?
and he replied with
>XNn=1an = a1 +XNn=2an ≤ a1 +XNn=2Z nn−1f(x) dx = f(1) + Z N1f(x) dx.
>>
x=5
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>>723622943
i agree
sq rt of 4x4 +3x3
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>>723622764
>if theres an infinite set of 0's and 1's is there an infinite set of 0's and 1's?
>being this stupid
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>>723622764
The answer I think is yes.
For example
101010101010...
Can be decomposed into
111111...
And
000000...
With the instruction that they alternate.
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>>723622764
Mathfag here. Not necessarily obviously, but yes it's possible. You're basically building a sequence containing only ones and zeroes.
To be completely accurate:
- If the sequence converges to 0 at infinity, then there are a finite number of ones.
- If the sequence converges to 1 at infinity,
then there are a finite number of zeroes.
- If the sequence doesn't converge, then there are an infinite number of both.
>>723623334
> 101010101010...
This is a perfectly suitable example that doesn't converge.
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>>723623757
Cool, 1010101010 anon here. What field of math deals with this kind of question?
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>>723623931
what does his friends response mean?
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>>723623268
this
why is this even a question
>>
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>>723622943
Memelord is pleased.
>>
>>723623931
That's a good question, actually infinite series are used in a variety of subjects so I'm not entirely sure what to answer... I know it's definitely a core concept in calculus, and especially when you start by defining real numbers from the ground up.
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