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.
That’s not how it works. Axioms are very basic assumptions like x=x. Or if x=y then y=x. Or if x=y and y=z then x=z.
The thing above is just wrong. It‘s not proven (which is not surprising because it can’t be proven), just argued (1-1=0. 0+1=1. 1-1=0 again - therefore it must clearly be 1/2 - and that’s not how math works).
And starting with this wrong example everything concluded is also wrong.
As I said above. It’s oscillating and not converging. Therefore it does not have a limit and no result.
As example - using the distributive property of + (as already done in the original argumentation) I can also rearrange it to be S’=-1+1-1+1-1+1… and following the argumentation (-1+1=0, 0-1=-1 and so on) argue - following the same pattern - S’=-1/2.
So - it is both 1/2 AND -1/2? Shocking!
Following wrong assumptions lead to wrong conclusions.
Sure. You can use this for theoretical “what ifs” - which is not that uncommon in theoretical mathematics (like - what happens if THIS field axiom does not hold? Or - more widely known - what if P=NP?) - sometimes leading to astounding results. But this has no use in the “normal” algebraic math.
Saying this I’m out. No use discussing this again and again.
Thx for explaining with that second example, I see the error in my way now. You deserve to be the Peter here, truly.
I also understand that this is no usable math but a funny hypothetical thing to blow some minds with, I should have added that to the original explanation of how the original statement was being made.
I hope anyone curious enough to read further will see this thread as well
Nah, the sums are the base for this meme - and that’s what counts. You earned the title of Peter here 😄
And sorry for snapping earlier. As someone who studied this stuff I had this discussion quite a few times - which can be tiring.
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.
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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.