Recent content by r731

As far as I know, HIV replicates itself at an exponential rate in a base b. For simplicity, let b = 2. For example, if one cell is infected, then HIV makes one copy of itself (since b = 2). And the cell dies to infect two new cells. These two new cells die to infect four new cells and so on...

An interesting theoretical topic would be a program that reduces one NP-complete problem in graph theory to another one. See Karp reduction.

Check out the twin paradox, and news sites for astronomy, such as this one, https://www.universetoday.com Imagine creatures in the form of neuro-clouds that live in space. Or think of the abducted sibling to be living in a planet where there is a much more advanced civilization than humanity's...

As far as I know topological spaces are preserved via homeomorphism. I doubt that a metric is required for a manifold.

I don't think so. Are there any points outside the 2-D Euclidean plane (the coordinate system)?

A boundary point P is a point such that any neighberhood centered around P contains a point inside the set and a point outside the set.

Check out the epsilon-delta definitions of limit and convergence.

It would be interesting to note that differentiation can be used as an operator for functions of R, while integrating the operand would mean taking the inverse of the operand.

A proposition can be viewed as a 0-ary boolean function. A predicate, in general, can be viewed as an n-ary boolean function. To give an example, let P(m,n) = "m walks to n". Then P(m,n) is a 2-ary boolean function - a function of two variables - that outputs 0 or 1.

The statement is false. Pick a = 4, then for all n, m that satisfy n*m = 4, n > 0 or m > 0. If n = -2 and m = -2, then n*m = 4, but neither of them is bigger than 0.

Question: Can heavy objects be used to operate light waves with smaller amplitude, or waves with high amplitude be used to operate objects with small mass? This is a diagram I drew that illustrates my point. Heavy objects are meant to be celestial bodies, and the light source generates a beam...

Let G be a graph where vertices are heavy planets and edges are forces between the incident vertices. A complete graph K6 of six planets (of different masses) has 15 edges, why don't the planets collapse to the center?

Say a person is infected with disease X. I suspect that it's possible for computers to learn the behavior of X via machine learning. This would lead to greater understanding of X. The unsupervised learning approach is pertinent to this. For another approach, say a new medicine Y is being...

Relabel e,a,b,c to [0],[1],[2],[3] respectively. It should make things easier to understand. Note that in the group [0] = [4] = [8] and similarly [1] = [-3] = [5] = [9] and so on.

I may be off. What frightens me is that if P=NP and any proof can be generated for an arbitrary proposition, then countless new theorems would be derived, notwithstanding theorems applicable in the sciences and engineering. Speaking of cryptography, if P=NP, it's not too hard to see that a...