Irrational Number

Proof method: Proof by contradiction

Proof method: Proof by contradiction

I was first presented with a proof by contradiction while I was studying Discrete event systems in Canada. And I was puzzled about it most day. I came to really like it though.

When we want to prove something by contradiction we assume that the statement we want to prove is false and then show that it leads to a logic contradiction at some point, therefore the statement must be true. Don’t be confused just yet. I will come to the examples.

Proof by contradiction is not limited to conditional statements like the the direct proof is. So we don’t need to have a proposition on the form if Q then P. Continue reading →

Posted by Kristian in Math, 11 comments

Project Euler 40: Finding the nth digit of the fractional part of the irrational number

I am currently sitting in a train, and writing this post since I solved problem 40 in Project Euler using pen & paper waiting for my computer to start up and get online.  It is not a terribly difficult problem to answer, at least it wasn’t for me. The problem reads

An irrational decimal fraction is created by concatenating the positive integers:

0.123456789101112131415161718192021…

It can be seen that the 12th digit of the fractional part is 1.

If dn represents the nth digit of the fractional part, find the value of the following expression.

d1 x d10 x d100 x d1000 x d10000 x d100000 x d1000000

Continue reading →

Posted by Kristian in Project Euler, 12 comments