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> it does make me think that infinity must be even since infinity can be divided into 2 pairs, each of which is of equal size since both are infinity. This is
by SideburnsOfDoom 4y ago
> it does make me think that infinity must be even since infinity can be divided into 2 pairs, each of which is of equal size since both are infinity.
This is true,
but the same is true of (infinity - 1)
Therefor infinity must also be odd.
- kccqzy 4y agoThe concept of "infinity - 1" doesn't exist. Subtraction isn't defined for ordinals. Furthermore even if you try to define it, it doesn't work for limit ordinals. If you are thinking about the difference between [0,1,2,3,…] and 0, [1,2,3,4,…] Then I regret to inform you the former is omega and the latter is 1+omega which is the same as omega. In other words attempting to subtract one from infinity by removing from the front results in infinity.
- SideburnsOfDoom 4y ago> In other words attempting to subtract one from infinity by removing from the front results in infinity. And I regret to inform you that if you read more carefully, you will find that my comment above makes use of that very same property of infinity. Not only do I already know it; that's the joke. Specifically, that statements about omega are also statements about 1 + omega. The parent post saying "I think that infinity must be even" is such a statement. Regardless of if it's true or not, well-defined or not, coherent or not, it's equally all that about (infinity - 1). Should I also spell out that an argument that "n - 1 is even" is also an argument that "n is odd" ?
- deleted 4y ago[deleted]