So... What you’re saying is... -1/12 is NOT the sum of all real numbers... AHAYWJODUABQLDUWVQPDUQNFPIWBLDIWBELWOHWJKSUFHQN shouts out to my pre-algebra teacher, i can tell her i beat an 11th grader in a debate although it was probably unfair cause i go to a private school for math
@sadandy , that video is a misleading video. Not saying it's false, just misleading. Source: Math major in college who's taken all the calcs and many more. @Timyus what are you even saying dude?
I wouldn't say that you completely beat me, it was just a mistake on my part calling natural numbers real numbers I don't understand why 90% of your argument is just trying to prove me wrong while you're not doing anything to try to prove yourself correct I also never said that I was 100% correct (though I never said I was incorrect either), I was just introducing the idea of how -1/12 is the only conceivable number that could possibly be the BIGGEST number. I'm not going to say it's not misleading, but it was mainly just to explain my point in a clearer manner. There have been many articles written and many debates had about this same topic. There have been mixed opinions in both the mathematics and physics communities. I've had discussions about this same topic with my AP Chemistry teacher, who majored in Physics and Chemistry, and he agrees with me; however, since it's more of an arbitrary mathematical proof, it may not be correct!
If that was your intent then you would be sadly mistaken. You really haven't proved nor brought forth any external information that actually proves me wrong, yet you just criticize my misuse of the term "real number" (which I have even brought up myself, I have stated in previous posts that I meant natural number, mind you), therefore you think my accidental misuse of the term makes me 100% incorrect I'd like to hear your explanation on why you think the sum of all natural numbers is equivalent to the origin
Yea the reason of the mixed opinion is due to the many ways to define the sum. Like they aren't actually saying the sum of all natural numbers converges to -1/12. I'm not saying thaBecause that's false. It's a divergent series, proven in many ways. Example: if we have 2 sequences a_n and b_n. If 0<=b_n<=a_n for all n while the summation of terms (terms from n=1 to infinity) in b_n diverges to +infinity, then a_n must diverge to +infinity as well. Take 1/n ( 1,1/2,1/3,....) =b_n and a_n=1,2,3,4, and so on. b_1 =1=a_1=1, and after that first term b_n is always <a_n (1/2<2, 1/3<3,...). Thus, 0<=b_n<=a_n is satisfied. The sum of all terms in 1/n is known as the harmonic series, and it diverges to +infinity. Therefore, a_n must diverge. Addition for natural numbers is also closed, so adding finite number of natural numbers cannot return a fraction like -1/12. However for infinite additions, it it's different allowing them their answer. When we talk about sums of divergent series, there's a lot of different ways to do things. They just used a way by assigning a sum to natural numbers that fit the experiment in physics. It's honestly whacky stuff. You should never just take it in as fact but question it as well. Prove your source that the sum of all real numbers is the origin. 8th grade math doesn't even give you a way to even start to think about doing it. Until you have taken calculus , you wouldn't be able to fathom how to try to add up sets of infinite numbers that are not enumerable. You can't order all real numbers from 1,2,3,... They are dense, meaning there exists a real number between any 2 real numbers (r1<r3<r2). Using that fact, you can say r1<r4<r3, r4<r5<r3, and so on. Thus, there is no way to order them.
Keep further replies relevant to the actual thread, any further off-topic posts will be removed. Thanks
Why would you say -1/12 is the biggest number? I might just not be understanding you correctly, and you might have a different definition when it comes to a "big number" but -1/12 isn't the largest number in size if thats what you mean. There is an infinite amount of numbers larger than -1/12
Don't take it seriously. The people in the video are assuming a diverging (meaning the partial sums of the numbers in the sequence 1,2,3,4,..... actually start to trend toward another number that's not infinity. Better yet, they do this by saying 1-1+1-1+1-1 trends towards 0.5 even though the series lim Sup=1, lim Inf=0. When lim Inf=/=lim Sup, it cannot converge) series can actually have a defined finite sum. It's only relevant for the use in physics when the use of the Riemann zeta function is necessary because the force between two plates cannot be infinite. Don't try to actually convince yourself that -1/12> all numbers because of the complex plane analytic continuation being applied to 1+2+3+4+..... edit: to be clear, they are basically redefining the equals sign as "associated with", not actually "equals." 1+2+3+4+...=/=-1/12. edit2: The physics experiment has to assume there is some unknown dampening effect, which is similar to how they use something called Abel's sums to assume 1-1+1-1+1....=1/2.