Recent content by Svein

Copyied from "Real Analysis" (H.L. Royden): These are topological spaces. T_{1}: Given two distinct points x and y, there is an open set which contains y but not x. T_{2}: Given two distinct points x and y, there are disjoint open sets O_{1} and O_{2} such that x\in O_{1} and y\in O_{2}. T_{3}...

Copyied from "Real Analysis" (H.L. Royden): These are topological spaces. T_{1}: Given two distinct points x and y, there is an open set which contains y but not x. T_{2}: Given two distinct points x and y, there are disjoint open sets O_{1} and O_{2} such that x\in O_{1} and y\in O_{2}...

I seem to remember that metric is a strong topological property. For weaker topologies continuity is defined as that the inverse funcion of open sets are open. Whether this is applicable in this case I cannot say on the top of my head.

What is "orthogonality"? You need to add some structure to your space in order to define it. The usual version is a Hilbert space, where you define a "scalar product" of two vectors. If that scalar product is 0, the vectors are said to be ortogonal.

If you disconnect from the Internet, can the so-called "AI" apps ace the Turing test? In 1955 the Eliza program was nearly there (no Internet then).

4 sides equal and both diagonals are equal.

A "cypher" is another term for something that is converted from a readable format to something that is not readable. The reader then needs a "key" to convert the coded text into readable format.

I think the relevant answer is the "bump function".

Ah - colur codes. I remember way bak when TV could be repaired and often had to. A common fault in a certain model was that the cathode resistor had a tendency to burn out. The standard replacement resistor was 1kohm (brown - black- red). One low-level repair guy was red-green color blind...

Also observe that 2^{n} = (1+1)^{n}=\sum_{i=0}^{n}\begin{pmatrix} n \\ i\\ \end{pmatrix} 1^{n-i}\cdot 1^{i}=\sum_{i=0}^{n}\begin{pmatrix} n \\ i\\ \end{pmatrix}

Look at the triangle. Observe that each element is the sum of the two elements above it (in your row, 6=1+5, 15=5+10, 20=10+10 etc.).

In predicate calculus A\Rightarrow B is defined as \neg (A \wedge \neg B) , or (using deMorgan) \neg A \vee B . Expressed in words: You cannot have A and not B, or the converse: If A is false, B can be anything.

Have you tried "ping example.com"? You may not have the applicable DNS. Or does your program need to know how to access DNS?

As far as I remember the speed of light in vacuum is determined by the formula c= \frac{1}{\sqrt{\epsilon_{0}\cdot \mu_{0}}}. The actual numerical value follows from that. BTW the speed of light in any environment is given by c = \frac{1}{\sqrt{\epsilon \cdot \mu}} where ε is the dielectric...

Thhis is the trouble with "objectified C". If you want to do this in C, you would put this code in a separate module and declare the pointer as "static" (which means that only code in that module can access it).