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bunnies wrote
Yes, a fraction is a rational number.
Is this actually true? 1/(2*pi) seems like a perfectly reasonable fraction to me. My intuitive feeling is that a fraction is just one quantity divided by another quantity, no matter the set membership.
flabberghaster wrote
Oh i thought i remembered them as being rational, and that irrational ones were invalid. But i was wrong.
Flabbergaster demolished by logic and reason
flabberghaster wrote
Yes, a fraction is a rational number. The rational numbers are the set Q such that for all x in Q, x = a/b for some integer a and b (b != 0).
Decimal notation is just a different way to write a rational number.
Since Q is closed under division meaning that a rational divided by a rational is guaranteed to return a rational number (except for division by zero), then having a fraction with a decimal in it is valid.