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Showing posts with the label mathematics

Gödel’s Incompleteness Theorem: The paradox

 Consider the following sentence: “ This statement is false ”  Is that true? 😧 If so, that would make this statement false. But if it’s false, then the statement is true.  By referring to itself directly, this statement creates an unresolvable paradox.  So if it’s not true and it’s not false—what is it?

Why can't you divide by Zero?

  In the world of math, many strange results are possible when we change the rules. But there’s one rule that most of us have been warned not to break: don’t divide by zero. 

A python approach to GOLDBACH’S CONJESTURE

Goldbach’s conjecture On 7 June 1742, the German mathematician Christian Goldbach wrote a letter to Leonhard Euler, in  which he proposed the following conjecture. Goldbach’s conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics.  Every  even integer greater than 2 can be expressed as the sum of two primes What is a conjecture ?😕😕😕 A Conjecture is a conclusion or proposition based on incomplete information, for which no proof or disproof has yet been found. Goldbach number A Goldbach number is a positive even integer that can be expressed as the sum of two odd primes.  Since 4 is the only even number greater than 2 that requires the even prime 2 in order to be written as the sum of two primes, another form of the statement of Goldbach’s conjecture is that all even integers greater than 4 are goldbach numbers. The conjecture has been shown to hold for all integers less than 4⨯〖10〗^18, but remains unproven considera...

Dichotomy Paradox

Zeno of Elea, an ancient Greek philosopher famous for inventing a number of paradoxes, arguments that seem logical, but whose conclusion is absurd or contradictory.  For more than 2,000 years, Zeno's mind-bending riddles have inspired mathematicians and philosophers to better understand the nature of infinity.  One of the best known of Zeno's problems is called the Dichotomy Paradox , which means, " the paradox of cutting in two " in ancient Greek.  It goes something like this: After a long day of sitting around, thinking, Zeno decides to walk from his house to the park. The fresh air clears his mind and help him think better.  In order to get to the park, he first has to get half way to the park. This portion of his journey takes some finite amount of time. Once he gets to the halfway point, he needs to walk half the remaining distance. Again, this takes a finite amount of time. Once he gets there, he still needs to walk half the distance that's left, which take...

Python: the language of future

Python is an easy to learn, powerful programming language. It has efficient high-level data structures and a simple but effective approach to object-oriented programming.