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comment Solving the recurrence $A_n = \sum_{k=1}^{n} 2^{k+1} A_{n-k}$
I wish Martin had asked this a few days earlier. I just assigned some similar problems to my linear algebra students and this one actually is much nicer than the artificial ones I came up with.
Feb
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revised Solving the recurrence $A_n = \sum_{k=1}^{n} 2^{k+1} A_{n-k}$
added 15 characters in body
Feb
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answered Solving the recurrence $A_n = \sum_{k=1}^{n} 2^{k+1} A_{n-k}$
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comment What's an example of an infinitesimal?
@CarlMummert please see this MO question to understand user72694's comment : mathoverflow.net/questions/227945/…
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comment Are there statements that are undecidable but not provably undecidable
@JDH's objection is correct but there is more. The implicit assumption is actually that ZFC+Con(ZFC) is $\Sigma^0_1$-sound: that this theory does not prove any false $\Sigma^0_1$-statement. If ZFC+Con(ZFC) is not $\Sigma^0_1$-sound then there is a Turing machine $M$ such that ZFC + Con(ZFC) proves that "$M$ halts" but $M$ doesn't actually halt...
Dec
23
comment Problems with introducing ordered pairs axiomatically
Andrej, this doesn't answer the question as posed. The OP is asking about a global pairing function, not about the existence of products, which only gives local pairing functions.
Dec
23
answered Problems with introducing ordered pairs axiomatically