>>12745254How? How does "3-1=1" contradict "3-1=2"? Where's the contradiction?
All it does is imply that "1=2", which, while stupid, is logically consistent. It implies a system where all finite numbers equal all other finite numbers.
>>12745183>>12746102Fair, OP didn't give a system, and seems like a brainlet. But what he's getting at seems to suggest one.
He asserts both that lim(?){1/n} equals a number, AND that said number isn't 0.
However, such a number then must be infinitely small. Lets call it "?"
Moreover, if it's not 0, then it doesn't have 0's multiplication properties. Ie:
2 * 0 = 0 , BUT, 2 * ? =/= ?
But how do we define ?, or 2?, or any such variation? OP also implies this by how he constructed "0.TTT"
Whereas "0.999..." is 9 * 0.111... = 9 / , "0.TTT" is 19 /
For these to be different numbers, as OP asserts, that implies that =/=
This means that we have two infinite values that do not equal each other.
We thus construct a system of infinitesimals "?"s, defined as the inverses of varying infinites ?, defined by different infinite sums.
This all lies on the assumption that infinite sums equal a definite number, and not all such infinite numbers are equal.
The standard way of writing limits subtlety treats "?" as a singular quantity. Even though infinity isn't a number. Infinitude is a property of a quantity. And in this case, the property of a new kind of number, the ?'s.
