This is one of my pet peeves in maths.
Although I do understand the concepts presented, the notion of "greater" makes no sense when applied to something without boundaries.
Yet it's used all the time.
Although I do understand the concepts presented, the notion of "greater" makes no sense when applied to something without boundaries.
Yet it's used all the time.
Let's imagine all the odd numbers: 1, 3, 5, etc. Now imagine all the even numbers: 2, 4, 6, etc.
Can we agree that there is an "infinite" amount of numbers in each of those groups?
Now imagine all the odd numbers and even numbers together. That's also infinite right?
Would you say there are more "all numbers" than just "all odd numbers", or would you say that there are an equal number of them? (hint: the answer is equal).
Take two sets A and B. If we can assign every element in A to a different one in B, we say that |A|≤|B|.
Makes perfect sense for normal, finite sets, right? As it happens, this definition extends to infinite sets as well.