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answered Examples of “Non-Logical Theorems” Proven by Logic
Jul
24
comment Can universal instantiation be used more than once?
If technique X can only be used once in a proof, and I use it to prove A implies B, and use it to prove B implies C, then I wouldn't be able to combine these proofs to show A implies C as that would require two uses, and mathematics would pretty well come to a halt.
Jul
20
awarded  Yearling
Jul
14
comment Why is the height of a heap defined as $\lg n$?
See mathworld.wolfram.com/Lg.html for some discussion of what the notation $\mathop{lg}$ (as opposed to $\log$ or $\ln$) means.
Jul
14
comment Are the real numbers really uncountable?
I'm not sure what the issue is @frogeyedpeas . When a mathematician says "there exists an x such that..." they're not saying "there exists an x, with definition Y, such that...". If you want to, you can study numbers with this property but that has no bearing on the existence of the other numbers.
Jul
14
awarded  Nice Answer
Jul
14
answered Are the real numbers really uncountable?
Jul
9
comment How do I know if I have imaginary numbers when using Newton Raphson Method?
I guess you're wondering what happens if you're trying to solve an equation that contains complex values, or from a complex starting point. The answer is that it gets complicated. Seriously complicated: chiark.greenend.org.uk/~sgtatham/newton
Jul
7
comment Integral of the square of a function
The integral can easily be non-negative even if the integrand is sometimes not real. Consider a function $f$ that takes a small imaginary value for a small region and otherwise takes large real values. Overall the real parts will dominate the integral giving a non-negative result.
Jul
6
answered Is $\infty = \frac{1}{0}$?
Jul
5
comment Axiom of Choice and finite sets
"How do I choose such an x?" is often a good question if you're writing a computer program. But in mathematics, if you want to use the existence of $x$ then tautologically you need only a proof that $x$ exists.
Jul
5
awarded  Nice Answer
Jul
5
revised Understanding matrices.
added 202 characters in body
Jul
4
answered Understanding matrices.
Jul
4
comment Understanding matrices.
That code isn't right. Maybe you mean newX = cos(angle)*oldX-....
Jul
4
revised What is the geometric meaning of this integral?
added 2 characters in body
Jul
3
answered What is the geometric meaning of this integral?
Jul
1
revised Second derivative of discrete function
This isn't discrete mathematics
Jul
1
suggested suggested edit on Second derivative of discrete function
Jul
1
awarded  Enthusiast