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Jul
12
comment How to prove that the Fibonacci sequence is periodic mod 5 without using induction?
@Timbuc How is it inductive? Because addition, multiplication by irrationals and exponentials are inductive?
Jul
12
comment How to prove that the Fibonacci sequence is periodic mod 5 without using induction?
I don't understand the talk about 'implicit induction'. The proof method asked for should not use an induction hypothesis, and they don't. Any implicit induction is like saying "Gaussian elimination inverts an $n\times n$ matrix" or "$2^n$ is total" are proved implicitly by induction because they involves natural numbers.
Jul
12
comment How to prove that the Fibonacci sequence is periodic mod 5 without using induction?
@Timbuc It is not necessary that $F_n$ be defined inductively; it could be defined using Binet's formula from the beginning and then later proved that the equation for $F$ in terms of smaller values holds. No necessary induction.
Jul
3
awarded  Good Question
Jun
13
comment Why is it that this gives a good approximation of $\pi$?
What is a reason and what is a coincidence? This is realted to the mathematical phenomenon of almost integers, calculations involving seemingly random irrationals that turn out to be almost an integer (your choice could be rearranged to say $\frac{\ln^2 11}{\ln 100 \pi} \sim 1$). A reasonable 'why' answer might come from equations that involve floors (like powers of the Fibonacci constant).
Jun
12
comment What are “instantaneous” rates of change, really?
To reword what others have said, 'instantaneous' is just a metaphor to help with intuition. In the metaphor, there's a contradiction, movement over no time at all which really isn't movement. So that's a problem with the intuition, not the formal mathematics.
Jun
10
awarded  Notable Question
Jun
9
revised What is the smallest unknown natural number?
added lower bound picture
Jun
2
comment Why doesn't the Taylor series always converge?
Can you give some of these well-known examples?
May
26
comment General solution to a system of non linear equations with a specific pattern
Have you tried solving less complex systems, for example all these systems without the first equation ($a^2 + b^2 + ...$), or just the first two equations? or where $x^i$ all equal 0? Those kinds of simplifications may (or may not) be easier to solve and may give hints on how to solve the bigger problems.
May
14
awarded  Excavator
May
14
revised Why the chi-squared statistic follows chi-squared distribution?
removed error
May
11
awarded  Nice Question
May
8
comment How many ways can $133$ be written as sum of only $1s$ and $2s$
Why isn't the answer about integer partitions $\leq 2$ rather than tuples with entries $\leq 2$?
Apr
27
revised Problem in deducing the number of onto functions
fixed grammar, tag
Apr
27
reviewed Approve finding the probability to get a diploma
Apr
23
comment A fun problem by Arnold using the Poincaré recurrence theorem
@rhetoricalphysicist: OK, I see the point now. Can you comment a hint as to how to use Poincare or even give an answer then?
Apr
23
comment A fun problem by Arnold using the Poincaré recurrence theorem
Why Poincare's recurrence thorem? Use Benford's law instead (hattip Travis).
Mar
23
comment Where did mathematicians learn how to do truth tables?
Are you saying there is evidence that some Greek philosophers had the concept of truth functions (functions whose inputs and outputs are something like true and false)_and_ graphical representation of truth tables (a tabular representation)? I don't doubt the first, but I do the latter. Also, the question I have is about the intellectual provenance of the truth-table display in modern mathematics, not the multiple possibly non-influencing reinventions across the world.
Mar
16
comment Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers
@user86418 the derivation after $x+1=2y$ is elementary. Getting to that point is also elementary but missing; just say where it comes from (why +1? Why 2y?)