It’s not a for loop, for loops don’t deal with infinity as far as I know.
How is this a break down? (I don’t know what you’re building.)
As in, the results 1 + 2 + 3 + 4 … = −1/12 is “obviously false” yet mathematically true. So the pattern of “if something is true in a very intuitive way than it must be mathematically true”, doesn’t hold in those kind of cases (as opposed to the 2 * 3 = 6 case, where mathematics correctly describe what we intuit to be true by saying the statement is correct, at least if you think of mathematics as a “language” in the “programming but running on wetware” sense.
I’m pretty sure appending a single number to an infinite series is not the same as appending a number to each of the terms (e.g. combining two infinite series as per my example).
But even if what you wrote were “correct” by the same token that the sum of the divergent series I mentioned is, it doesn’t have much to do my point in that paragraph, which was to say that these kind of statements make no intuitive sense but yet have some correctness to them.
It’s not a for loop, for loops don’t deal with infinity as far as I know.
As in, the results 1 + 2 + 3 + 4 … = −1/12 is “obviously false” yet mathematically true. So the pattern of “if something is true in a very intuitive way than it must be mathematically true”, doesn’t hold in those kind of cases (as opposed to the 2 * 3 = 6 case, where mathematics correctly describe what we intuit to be true by saying the statement is correct, at least if you think of mathematics as a “language” in the “programming but running on wetware” sense.
This only seems to be the case because the equals sign is redefined in that sentence.
I’d wouldn’t say it’s “true”.
Unless you think 1=0.
Proof:
[1] x = 1 + 1 + 1 + ….
Subtract 1 from both sides.
[2] x-1 = 1 + 1 + 1 + …
Substitute using [1].
[3] x-1 = x
Subtract x from both sides.
[4] −1 = 0
Multiply both sides by negative 1.
[5] 1 = 0
I’m pretty sure appending a single number to an infinite series is not the same as appending a number to each of the terms (e.g. combining two infinite series as per my example).
But even if what you wrote were “correct” by the same token that the sum of the divergent series I mentioned is, it doesn’t have much to do my point in that paragraph, which was to say that these kind of statements make no intuitive sense but yet have some correctness to them.
They are correct if you accept a strange premise like “infinity = 0” or ignore mistakes, like the one I made in the proof above.