Why? I don't see why you would care about this inequality. That limit is the definition of asymptotic... There's really nothing to prove if...
I'd expect it to be in Ramanujans notebooks, but wherever you found it, does your library not have an interlibrary loan system? This asymptotic...
The basic steps: 1) count the number of zeros contained in a rectangle with corners 0,1,1+i*T,i*T, where T is the height you want to go up to....
I've been reading what you've been writing. The part you bolded is not what you've been claiming, at least it's not what you've been writing. You've...
No kidding stuff beyond grade 9 is needed to justify the steps. I did say that the steps in the above proof are not justified even for a high school...
Until you define what you mean by "a random point on the number line" this question is vague and unanswerable. Ask them what distribution they are...
The nested invtervals you construct aren't necessarily contained in your bounded set so you have no way of knowing if the point they have in common...
The cluster point need not be in the set. You should be able to find an example where this is the case without too much trouble. Where is your...
I had to cut short before I finished my post earlier and wanted to expand on a couple of things. That's fine, but you don't give indication on...
What has been omitted then? Alright, I'll state it. If you have a terminating decimal, adding zeros after the last digit doesn't change the number....
You're trying to show F(1) is equivalent to F(2), F(2) is equivalent to F(3) and so on? What you have is fine (provided you already know bounded half...
I'm devastated. Multiple times in this thread I've told you how to justify the digit manipulations. Multiple times you've totally ignored this and...
Maybe a stand alone proof of some digit manipulations is in order? I hope against all hope that you willthrow off your tradition of ignoring what I...
I never said you believed otherwise. I've explained what was wrong with your "8.99...1" attempt and the others. I went through in more detail...
Yes. Same theorem I was refering to above. It's valid for any series.
Apply theorem 3.3 from Rudin again to the sum of the limits on the right to get (no idea why the \infty isn't rendering properly): <img...
What you are missing is that we can evaluate the limits in another way that corresponds to the proof you are objecting too. I'll just take a second...
I've been meaning to come back and respond to this bit, but it would be a pain to go into the detail you require without latex, so here it is. I just...
I don't have Boas on hand, what are they calling a "preliminary divergence test"? I'd guess from your post they are refering to the theroem that...
The infinite series are exactly what justify the manipulations of the digits. The decimal notation is just a shorthand for these series. The whole...
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