Hello/Goodbye Thread #4
- Thread starter Cam
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Joshua Farrell
FP's Housekeeper
Hey everyone!
Joshua Farrell
FP's Housekeeper
Ridley said:
Hi Ridley! How are you?
Joshua Farrell
FP's Housekeeper
Ridley said:
I am good. 🙂 Enjoying a little bit of Monty Python.
Joshua Farrell
FP's Housekeeper
Hey Gio!
Joshua Farrell
FP's Housekeeper
Hello Matt! How are you?
Joshua Farrell
FP's Housekeeper
Hey Gio! I am doing pretty good here. 🙂
Joshua Farrell
FP's Housekeeper
Hey Aaron! How are you?
Hello FP! Allow me to share some discrete maths!
Prove √2 is irrational.
Suppose √2 is rational.
Therefore, there exists a and b elements of the integers where b is non-zero so that √2 = a/b where a and b do not have any common factors (lowest possible terms)
Therefore 2 = a²/b²
2b² = a²
a² is even, therefore a is even
Therefore, there exists r an element of integers so that a = 2r
So we have 2b² = (2r)²
2b² = 4r²
b² = 2r²
b² is even, therefore b is even
a and b both have the same factor of 2, since they're even
This means a/b is not in lowest possible terms, thus a contradiction.
Therefore, √2 is irrational.
Prove √2 is irrational.
Suppose √2 is rational.
Therefore, there exists a and b elements of the integers where b is non-zero so that √2 = a/b where a and b do not have any common factors (lowest possible terms)
Therefore 2 = a²/b²
2b² = a²
a² is even, therefore a is even
Therefore, there exists r an element of integers so that a = 2r
So we have 2b² = (2r)²
2b² = 4r²
b² = 2r²
b² is even, therefore b is even
a and b both have the same factor of 2, since they're even
This means a/b is not in lowest possible terms, thus a contradiction.
Therefore, √2 is irrational.
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