Different orders of infinity are e.g. the Natural Numbers and the Rational Numbers. There is an infinite amount of Rational Numbers "between" each sequence of Natural Numbers. — Echarmion
Fdrake already answered this, but if bijections, injections and surjections aren't familiar to you, here's a one way to look at it:Let's take two infinite sets of numbers:
1. ...1,2,3,4,5,6,7,8,9,10,11 .....
2. .... 2,4,6,8,10,12,14 ......
So both sets follow a very obvious pattern.
Question:
Does the first set constitute a bigger infinity than the second one, as, let's take the interval (1;4) for example, the first set includes four numbers (1,2,3,4,) of this interval whereas the second one only includes two (2,4)? — Gilbert
I'm assuming that this is a trivial question, but nonetheless it just occured me and I can't think of a way to approach it. If my mathematical premises are wrong (which could very well be the case) please correct me.
Let's take two infinite sets of numbers:
1. ...1,2,3,4,5,6,7,8,9,10,11 .....
2. .... 2,4,6,8,10,12,14 ......
So both sets follow a very obvious pattern.
Question:
Does the first set constitute a bigger infinity than the second one, as, let's take the interval (1;4) for example, the first set includes four numbers (1,2,3,4,) of this interval whereas the second one only includes two (2,4)?
Furthermore, applying this reasoning to the whole sequence, can the equation: Infinity (set 1)= Infinity (set 2) x 2 be infered from that?
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