Recent content by Atran

Against waves of other wavelengths. Imagine an object surrounded by a "sphere" of waves of a certain wavelength, that shields the object from waves of other wavelength. Am I correct in saying that x-rays can penetrate radio-waves while the reverse is not true?

Hi. I've got two questions. Is it true that waves with longer wavelengths are handled easier? Think of a scenario where radio-waves insulate a solid object (in a lab for example). How can this be done? Given my understanding, waves don't travel around the environment uniformly.

5+5 equals π in Z_{\pi}. An isomorphism that takes a member of Z to give a member of Z_{\pi} could be: f(b) = f(b_n{10}^n + b_{n-1}{10}^{n-1} + ... + b_1{10} + b_0) = a_n\pi^n + a_{n-1}\pi^{n-1} + ... + a_1\pi + a_0, where b is expanded to its decimal representation first. I don't worry about...

If I remember correctly, given a decimal expansion of a number, substitute powers of \pi for powers of ten. In other words, 127 = 10^2 + 2*10 + 7. After substitution, it becomes \pi^2+2\pi+7. Note that the latter is no rational number but it is a member of Z_\pi.

Yes.

This is how I thought to set up the group, though I did not go through it thoroughly. 0 in Z_\pi corresponds to 0 in Z. \pi in Z_\pi corresponds to 10 in Z. 2\pi in Z_\pi corresponds to 20 in Z. 3\pi in Z_\pi corresponds to 30 in Z. \pi^2 in Z_\pi corresponds to 100 in Z. 2\pi^2 in Z_\pi...

The rational numbers are not in the group; integers are rational numbers. On the other hand, 1+1 and 2 are the same number in, say for example, group (Z_5,+).

The elements of the group are not rational numbers. Hence 11 is not in the group. 11\pi in Z_{\pi} equals \pi^2+\pi and maps to 11 in Z.

A proper number is expressed in \pi in a similar way as a decimal integer is expressed in base 2. For example, 4375_{\pi} = 4{\pi^3}+3{\pi^2}+7{\pi}+5. The only exception I make is that the 10 digits are included when expressing a number with \pi. To clarify, the first positive such numbers are...

I was just reading about DNA sequencing. In my view, DNA can be modeled into an ordered sequence of nucleobases, as if the two strands were joined into a single strand (just like in RNA). The first half of the sequence models the first strand. The four nucleobases are numbered from 0 to 3...

I want somebody to prove this wrong, by finding a counter example. And I'm really sorry, I forgot to mention that i must not be divisible by any of the primes found in the product p(x). So again, 1 < p(x) ± 2*i < (p(x+1)/p(x))2 where p(x) is the product of the first x odd prime...

Hi! Say p(x) is the product of the first x odd prime numbers (e.g. p(4)=3*5*7*11) and i is at least one. Then consider: 1 < p(x) ± 2*i < (p(x+1)/p(x))2 My hypothesis is that the above formula, obeying the restrictions, always produces a prime number. For example if x=3 and i=13, then...

Hi. I don't understand how a solution to a linear system is obtained (for example geometrically; don't consider the substitution method and elimination), and I am feeling very frustrated. Say I have the following equations: y = x + 5 b = 2*a (the relation remains the same even if I change...

Thank you for your response. I'm thinking to stick with the precedence level above that of multiplication. Instead of starting a new thread: I consider a value to be a computed or assigned number or quantity. What's the difference between number and quantity? What exactly are number, quantity...

Hi, Does the author mean that −3 × 4 = 0 − 3 × 4 = −(3 × 4) or else? I consider the minus-sign to be a unary operator, which is preceded by multiplication and division. Am I thinking right?