3 ms·
The 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 ordinal
by kccqzy 4y ago
The 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]