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Jun
24
comment Why do calculus students learn to think of the derivative as a limit?
How else would you define it?
Jun
20
comment How to solve $2^x+e^x=400$
@HenningMakholm: As an extreme example, consider Fermat's Last Theorem. Easy to state, but took 358 years to prove.
Jun
20
comment Why isn't the empty set an element of $A \times B$, while it is a relation from $A$ to $B$?
If you're a computer programmer (in a statically-typed language with templates/generics), it may help to think of the × operation as the function Set< Pair<T, U> > CartesianProduct(Set<T> a, Set<U> b). The return value can be an empty set, but it can't contain an empty set because then the type would have to be Set<Set> instead of Set<Pair>.
Jun
4
comment Name of the highest power of 2 smaller than or equal to a given number
"Two to the Power of the Floor of the Base-Two Logarithm" = TPFBTL of x, pronounced kinda like "top of bottle".
Jun
2
comment Show that the question “Is there life beyond earth?” is decidable
The question can straightforwardly be answered by the Python (a Turing-complete language) expression any(obj.location != Earth and obj.alive for obj in universe()). The only hard part is iterating every object in the universe. But if you assume a finite universe, it's theoretically possible.
Jan
26
comment Can you be 1/12th Cherokee?
@Keavon: Technically, the protagonist of that song is his own step-grandfather, not his own biological grandfather.
Dec
30
comment Why rationalize the denominator?
@Ooker: Note the "floor" brackets.
Sep
12
comment In plain language, what's the significance of a field?
@Hal: Not always. Another thing that would keep a field from having less/greater than is the numbers being conceived of two-dimensionally. Think of $\mathbb{C}$.
Jul
25
comment inverse trigonometric equation $\displaystyle \tan^{-1}{x}+\cot^{-1}{x}=\frac{\pi}{2}$
Hint: $\cot x = \tan(\frac{\pi}{2} - x)$.
Jul
16
comment Are all existence proofs by contradiction?
Related: math.stackexchange.com/questions/427078/is-0-a-field
Jul
8
comment Calculate $\sum_{k=1}^n \frac 1 {(k+1)(k+2)}$
@Elimination beat you to it by 22 seconds.
Jul
4
comment How to distinguish walking on a sphere or on a torus?
@dotancohen: Even if they could look up, people living on the outer parts of Planet Doughnut wouldn't have a view of the hole.
Apr
20
comment Kid's homework: 4 equations 5 unknowns? Going crazy!
@metacompactness: Not necessarily. For example, there could be half-siblings on this trip, with 1 father and 2 mothers. Or cases where one parent is unable to attend.
Apr
5
comment Derivatives of exponential functions
There's no $x$ in your function. Did you mean dt instead of dx?
Apr
5
comment How can a piece of A4 paper be folded in exactly three equal parts?
It would be interesting to see an answer that relies on the $\sqrt{2}:1$ ratio of ISO paper sizes.
Mar
29
comment Why is there a different button for 'minus' and 'negative' on a calculator?
@Rahul: Based on your comment, I assume that you have an RPN calculator. However, I've also seen distinct - and buttons on infix-notation calculators like the TI-8x series, on which there's no obvious need to distinguish them.
Mar
29
comment Why is there a different button for 'minus' and 'negative' on a calculator?
This doesn't really answer the question. Although unary and binary minus are indeed distinct operations, a lot of programming languages, spreadsheet programs, etc., do manage to use the same symbol - for both of them.
Mar
29
comment Can a piece of A4 paper be folded so that it's thick enough to reach the moon?
Assuming a typical 0.1 mm thickness, how large would a sheet of paper need to be so that it could be folded 42 times?
Mar
28
comment Can a piece of A4 paper be folded so that it's thick enough to reach the moon?
1L << 42 is faster than calling a function ;-)
Mar
28
comment Can a piece of A4 paper be folded so that it's thick enough to reach the moon?
Just to verify, I measured a package of 500 sheets of paper, and it was about 5 cm thick. So, 0.1 mm per sheet is a good estimate.