Fractals are geometrical objects found in nature. They can also be drawn experimentally and mathematically. Clouds, lightning, and coastlines are natural fractals. Solitons are physical fractals. Mandelbrot set, Cantor set, Julia set, and Sierpinski triangle. we draw below the latter fractals in Python.
Q&A Session With the Bot: ACT ONE, SCENE 4
System down. ACT ONE, SCENE 5user logging in.fazal: Sorry yesterday the system was down.friend 1: How so?fazal: Well, many people are asking questions. I reply to them all simultaneously.friend 1: How so?friend 1 again: How could you manage to respond to everyone simultaneously?friend 1 again & again: Are you god?again friend 1: How so?again &... Continue Reading →
Q&A Session With the Bot: ACT ONE, SCENE 2
user logging in.friend 1: Yes sorry, last week you were telling me about antigravity. Should I ask the question again or do you have it in your memory?fazal: Well, I keep questions in my memory. However, a memory may be deleted at the user’s request.friend 1: Does a delete mean an absolute delete or do... Continue Reading →
Violation of Induction Hypothesis
Definition of an inductive set A subset A of the real numbers is said to be inductive if it contains 1, and for every element x in A, the number x + 1 is also in A. Here we show that a product set is not inductive. We shows that if C is subset of... Continue Reading →
A Finite Set of Numbers Is Incomplete Unless Infinity Is Assumed
In this post we explore how infinity shapes the number system. Without infinity the number system would be incomplete. I would like to explain this with examples. Consider a set of two integers {1,2}. I want to multiply them element by element, we get A= [1, 2] B= [1, 2] N= A × B= [1,... Continue Reading →
A Formula that Sends Primes Into Integers And Composites Into Fractions
Here we introduce a formula that sends primes numbers into natural numbers and composite into fractions. L(n)=π(n) +(n-pπ(n))/Δ where π(n) is the prime-counting function and Δ is the gap between two consecutive primes. We calculate the first few numbers. L(1) = 0, L(2) = 1, L(3) = 2, L(4) = 2.5, L(5) = 3, L(6)... Continue Reading →
Algebraic Proof That Two Is the First Prime
Theorem. It is algebraically proved that 2 is the first prime. Proof. Suppose that p1 is the first prime. Then p2 = p1 + 1 is the second prime. because no two consecutive numbers share the same prime factors., Suppose that c1 = p2 + 1 is another integer. Then it is possible to write... Continue Reading →
Who Says that Primes Have No Formula
Who says that primes Have no formula And that they are random We all know that Primes are in a set And that set is P Let 1st prime be p1 2nd be p2 3rd be p3 And then so on We don't care What their values are What we care Is that they come... Continue Reading →
2 Is Odd
2 is odd The turn of 2 Is odd 1st non-negative integer is 0 2nd is 1 3rd is 2 The turn of 2 Therefore, is odd Prime after prime Each prime Is odd 2 is odd Because its turn is odd Other primes are odd Because they're odd By nature
What Is Atom in a General Sense?
Atom is something that has no substructure. This means other things can be expressed in terms of atoms but they cannot be expressed of something smaller than them. The atoms of physical bodies are quarks and leptons. An electron is an elementary particle that does not have a substructure. However, a proton is made of... Continue Reading →