104 reputation
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location United States
age 32
visits member for 1 year, 8 months
seen 6 hours ago

I'm earning my PhD in mathematics and have been employed as an analyst since graduating college in 2003.


6h
awarded  Talkative
7h
awarded  Citizen Patrol
20h
comment Number of necessary stickers to complete a sticker album
Did @SteveKass answer your question by referring you to the Coupon COllector's Problem? Steve, or you, or I (or anyone else if he declines) should put it as an answer below, so it can be accepted.
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comment Number of necessary stickers to complete a sticker album
It looks like you and I were making edits at the same time at one point. Your latest edit to add $\binom{c-1}{t-1}$ and $\binom{c+t-1}{t-1}$ didn't make it into my edit which you just accepted.
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revised Number of necessary stickers to complete a sticker album
Attempted to rearrange things to help the OP end up with an easier to read question.
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comment Number of necessary stickers to complete a sticker album
Take a look at those changes. I don't want to change your meaning, but I think this order will help people understand your meaning better.
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suggested suggested edit on Number of necessary stickers to complete a sticker album
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comment Number of necessary stickers to complete a sticker album
Part of my confusion is that you've labeled an entire paragraph with your $1$, but you refer to it as if you've labeled a single equation. Also, if I understand correctly, that paragraph is part of your "this is what I tried that didn't work"? If that is the case, may I try my hand at rearranging a bit? If I bungle your intent, I believe you'll have the chance to reject my edit.
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comment Number of necessary stickers to complete a sticker album
While your formula are not clear to me, I believe I get the gist of the English, as I've asked myself (and solved) the same problem more than once. I don't recall the answer right now, but I can tell you that as $c \to \infty$, your probability approaches $1$, but never arrives there.
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comment Number of necessary stickers to complete a sticker album
Still trying to make sense of your question. Since you reference a mysterious "of $(1)$", but only at the end label something $(1)$, it leads the reader to think you're referencing something in a text somewhere, or a notion you were taught in a class that you think is standard. References to something should always come after that thing has been defined/labeled (or occasionally immediately before). Lastly (and I'm not picking on you, trying to improve your chances of getting a good answer), it's not clear to me what you're labeling $(1)$ and what that paragraph means.
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comment Number of necessary stickers to complete a sticker album
I think your lead-in "Consider a sticker album with $t$ stickers" is misleading. This puts the reader in the frame of mind thinking that you already have $t$ stickers and you bought $c$ more, but you seem to use it as if there are a total of $t$ unique stickers that one could collect.
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comment If there are obvious things, why should we prove them?
+1 for great philosophy. -1 for not really answering the question.
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comment If there are obvious things, why should we prove them?
@MichaelT I don't take often to mean the majority, or even a large minority of the time. I take it to mean that "it crops up often". If one were to consider 1,000 different concepts in a month, and once a month something that seemed obvious at first, but later turned out to not be so obvious, that once a month occurrence would still be often.
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comment If there are obvious things, why should we prove them?
@MarioCarneiro Your statement that there are twice as many elements in $\Bbb Z$ as $\Bbb N$ is exactly wrong. Neither of them have a finite number of elements, so both are infinite. There are many different cardinalities (sizes) of infinity, and there are no two different sizes of infinity where one is exactly twice the other. $\Bbb N$ and $\Bbb Z$ have exactly the same cardinality, exactly the same size, and exactly as many elements as each other. This is exactly what's meant by $| \Bbb Z | = | \Bbb N |$
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revised Prime factorization of 1
@ncmathsadist I think adding "unique" is a significant contribution to your answer.
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suggested suggested edit on Prime factorization of 1
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comment Why do we call primes, and not the number one, *the atoms of numbers*?
Additionally, the additive "periodic table" $\{1\}$ is pretty boring compared to $\{2,3,5,\dots \}$. Take that chemists, our periodic table is infinite.
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accepted How do I show a mapping is a homomorphism?
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answered How do I show a mapping is a homomorphism?
Apr
15
comment How does the base of a group determine the “sort” of the elements in the group
That's about what I figured out. It's the some kind of sort after that's frustrating me. As a mathematician I'm not too satisfied with Mathematica. I think it should be called Engineerica.