Smith1776 wrote: ↑
Sun Mar 29, 2020 8:53 am
technovelist wrote: ↑
Sun Mar 29, 2020 8:41 am
Smith1776 wrote: ↑
Sun Mar 29, 2020 5:41 am
I am 90% of my way through finishing the last math assignment I will ever have to do... for the rest of my life!
By the way, infinite sequences and series suck. Like... a lot. Did you know that the sum of all positive integers from 1 to infinity is -1/12
? Okay, fine, that's actually pretty interesting. Still, they suck. A lot.
I'm pretty sure that
isn't right. I suspect that is an example of how not
to sum infinite series.
But of course there really isn't any such thing as an infinite series. That is just an abstraction that can be useful sometimes and wildly off-target other times.
It is unbelievable but true. I've been studying this section for a good while and so much of it still doesn't make sense to me.
https://medium.com/cantors-paradise/the ... cc23dea793
The mathematician in the youtube video literally does the proof, and I still don't have my mind quite wrapped around it.
No it isn't true. It's an excellent example of why you can't treat "infinite series" like actual things.
Again, they are abstractions, not reality.
Here's a simpler example which is equally valid:
Assume that we have two variables a and b, and that: a = b
Multiply both sides by a to get: a2
Subtract b2 from both sides to get: a2
= ab - b2
This is the tricky part: Factor the left side (using FOIL from algebra) to get (a + b)(a - b) and factor out b from the right side to get b(a - b). If you're not sure how FOIL or factoring works, don't worry—you can check that this all works by multiplying everything out to see that it matches. The end result is that our equation has become: (a + b)(a - b) = b(a - b)
Since (a - b) appears on both sides, we can cancel it to get: a + b = b
Since a = b (that's the assumption we started with), we can substitute b in for a to get: b + b = b
Combining the two terms on the left gives us: 2b = b
Since b appears on both sides, we can divide through by b to get: 2 = 1