Search for notes by fellow students, in your own course and all over the country.
Browse our notes for titles which look like what you need, you can preview any of the notes via a sample of the contents. After you're happy these are the notes you're after simply pop them into your shopping cart.
Document Preview
Extracts from the notes are below, to see the PDF you'll receive please use the links above
Providing √2 irrational
That's a great proof! You've successfully shown that assuming √2 is rational leads to a
contradiction, thus proving that √2 is indeed irrational
...
Assume √2 is rational, so √2 = a/b (where a and b are integers with no common factors)
...
Square both sides: 2 = a^2/b^2
...
Clear the fraction: 2b^2 = a^2
...
Analyze the equation: a^2 is even, so a is even (a = 2k)
...
Substitute a = 2k: 2b^2 = (2k)^2 => b^2 = 2k^2
...
Conclude b is even (since b^2 is even)
...
Reach a contradiction: Both a and b are even, so they have a common factor of 2,
contradicting the assumption of simplest form
...
Conclusion: √2 is irrational
...