Archive for the ‘Discrete Mathematics’ Category

How many primes are there?

February 17, 2009 Leave a comment

Prime number is a natural number greater than 1 and has exactly 2 divisors, 1 and itself.

The first few prime numbers are 2, 3, 5, 7, 11, 13, 17 …

The question is, How many primes are there? or in other words, is there a finite number of primes?

The answer is NO, there are infinite number of primes and we are going to prove this below together.

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√2 is irrational

February 15, 2009 6 comments

Prove that √2 is irrational number i.e. it can not be represented as a fraction a÷b where a and b are integers, b>0.

This is a very clever proof as a practice on proof by contradiction.

If you believe that √2 is a rational number, then I’ll ask you to come with this fraction a÷b but first reduce it to lowest terms. And I’ll convince you at the end that a and b must be both even. Does this mean you are a liar? 😉 – No it just means that there is a contradiction and thus √2 can not be rational (and that a÷b you have suggested is a fake! 😉 ).

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Discrete Mathematics?

February 15, 2009 1 comment

Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite mathematics are countable sets, such as integers, finite graphs, and formal languages. The term “Discrete Mathematics” is therefore used in contrast with “continuous mathematics,” which is the branch of mathematics dealing with objects that can vary smoothly (and which includes, for example, calculus). Whereas discrete objects can often be characterized by integers, continuous objects require real numbers.

Funny Histroy

Professors in the last 10 years would say we should not have a Discrete Math course because we have a course in Logic, We should not have a Discrete Math course because we have a course in Combinatorics, ….
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