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Apr
26
comment Shouldn't all alternating series diverge by the diverge test?
To be precise, the limit of the sequence $b_n$ is 3/4, but the sequence $a_n$ does not have a limit. You're right that when it comes to determining whether or not a sequence converges to 0, sign isn't an issue.
Apr
26
answered Shouldn't all alternating series diverge by the diverge test?
Apr
19
answered How do you create an alternating series with the sign being the same twice in a row?
Apr
10
answered I don't understand what a “free group” is!
Apr
3
comment Is there such a thing as backwards sigma?
But that's why I said "if it appears twenty times in your summand". In your two examples, the subtraction only appears once. If it appeared twenty times, it would start to get cumbersome.
Mar
26
comment Is there such a thing as backwards sigma?
Doing subtraction like this isn't necessary the best notation. If $(11 - i)$ appears twenty times in your summand, it's probably best to think of an alternative.
Feb
10
comment What is the flaw of this proof (largest integer)?
That's correct, Chris.
Aug
31
comment Relation between XOR and Symmetric difference
True. Restating myself more precisely: there's a one-to-one correspondence between the subsets of a set and the predicates on that set, but in a set theory such as ZFC, not every predicate defines a set.
Aug
27
awarded  Good Answer
Jul
19
awarded  Yearling
Jul
9
answered W. Mückenheim claims a severe inconsistency of transfinite set theory; true?
Jul
9
comment In a vector space in finite dimension, all vectors which are not colinear, are orthogonal. True or false?
The word "orthogonal" is not defined for vector spaces, so the question uses undefined terminology, and must be modified before it makes sense. Your argument is valid if you replace "all vectors that are not collinear are orthogonal" with "for every pair of vectors that are not collinear, there is an inner product for which they are orthogonal".
Jul
6
answered Properties that are true for finite sets but are (non-trivially) false for infinite sets
Jul
2
comment Why are conformal mappings necessarily 1 to 1?
Well, both the unit disk and the upper half-plane have the same cardinality, so there's no problem there. The upper half-plane has infinite area, while the unit disk has finite area; but biholomorphic functions don't have to preserve area, so that's not a problem, either. If you're familiar with an order-preserving bijection between the open interval $(0,1)$ and the entire real line, this biholomorphic function acts much the same way.
Jun
11
comment Conflicting limit answers using calculator and wolfram alpha
I don't think this answer is quite correct. A calculator that uses floating point numbers is unlikely to round a very small number to zero. My guess is that $\sin 0.0000000001$ and $\tan 0.0000000001$ are so close together that the calculator rounded the two numbers to exactly the same number, meaning that it subtracted two identical numbers, getting zero.
May
21
answered Floor function to the base 2
May
11
awarded  Popular Question
May
5
revised Number of Distinct Axiomatic Systems
Describe construction of theories with models of arbitrary finite size
May
5
answered Simple Adding and Subtracting algorithm to get a current amount
May
5
comment Number of Distinct Axiomatic Systems
It can be written out explicitly by an algorithm. Here's a first-order theory where every model has exactly four elements: "a ≠ b. a ≠ c. a ≠ d. b ≠ c. b ≠ d. c ≠ d. For all e, e = a or e = b or e = c or e = d." You can do the same for any number n: think of n constants, then write down axioms asserting that no two of the constants are equal to each other, and then write down one more axiom asserting that everything equals one of the constants.