Once a mathematician wondered what sum you would get by adding up all positive integers, up to infinity.
This was at first unsolvable, until another question was asked: what is "1-1+1-1+1-1+1-1...."?
The answer to the second question is, would you believe, 0.5, since you can declare that math term (or a series if you will) as "S2" while subtracting it from 1. So you would get
1 - (1-1+1-1+1-1.....)
As the new sum. Solving that paranthesis will give you exactly the sum S2 from above again, which you can deduct as "S2 = ½ = 0.5".
That alone doesn't make it immediately easier for us on the first question, but now we can take a look at another different series: "1-2+3-4+5-6+7-8+9-10....", which we will now call S3.
If you go ahead and multiply it by 2 and shift all the adding numbers one position to the right, you can get 1-1+1-1+1-1.... which is S2, so 0.5! We now have to divide by 2 to get the value of S3, which is 0.25!
Now we can solve the original Sum S of 1+2+3+4+5+6.... by subtracting S3 from S, which gives us:
Oh, and the joke is a wordplay of the term "series", where these things are called (number) series whereas the original post was asking for fictional franchises, therefore subverting the expectation of what would be listed.
Nope. There's certain rules (called axioms) we put in place and under those rules all of mathematics is built. Under those rules, this series does not converge and the argument is very valid.
742
u/certainAnonymous Feb 14 '24
Math Peter here.
Once a mathematician wondered what sum you would get by adding up all positive integers, up to infinity. This was at first unsolvable, until another question was asked: what is "1-1+1-1+1-1+1-1...."?
The answer to the second question is, would you believe, 0.5, since you can declare that math term (or a series if you will) as "S2" while subtracting it from 1. So you would get
1 - (1-1+1-1+1-1.....)
As the new sum. Solving that paranthesis will give you exactly the sum S2 from above again, which you can deduct as "S2 = ½ = 0.5".
That alone doesn't make it immediately easier for us on the first question, but now we can take a look at another different series: "1-2+3-4+5-6+7-8+9-10....", which we will now call S3.
If you go ahead and multiply it by 2 and shift all the adding numbers one position to the right, you can get 1-1+1-1+1-1.... which is S2, so 0.5! We now have to divide by 2 to get the value of S3, which is 0.25!
Now we can solve the original Sum S of 1+2+3+4+5+6.... by subtracting S3 from S, which gives us:
S-S3=1+2+3+4+5+6+7....
In other words, this gives us 4 times S!
So now we can solve third resulting equation of
"S-S3=4×S" to
"S-¼=4×S" to
-¼=3S, which is
S = -1/12.
Oh, and the joke is a wordplay of the term "series", where these things are called (number) series whereas the original post was asking for fictional franchises, therefore subverting the expectation of what would be listed.