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31 Jan 2014, 01:41
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Disclaimer: please do NOT apply this on the test!!! Very much out of scope!!!
What would you say is the value of 1 + 2 + 3 + 4 + 5 + ... to infinity ? I bet you'd be surprised to know it's:
\(-\frac{1}{12}\)
31 Jan 2014, 12:49
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Bunuel
Bunuel,
This is great! It's funny the way those guys, physicists, talk about how the sum is "really" -1/12. Yes, that's really what it would be for Physicists, especially for String Theorists, but not at all what it would be for Mathematicians! This entire discussion really gets into some very profound areas --- the difference between the math used in Physics and the math used in pure Mathematics; the difference between operational mathematics and mathematical rigor; the deeply ambiguous nature of infinity and exactly what it means; the relationship of mathematical ideas to the physical world; etc. It think most students here would not appreciate that mathematics, far from being a totally cut-and-dry unambiguous field, is at higher levels very much a matter of multiple possibilities governed by convention and tastes. All this is well beyond the GMAT or anything particularly relevant to the business world, but it certainly is fascinating.
Thanks for posting this.
Mike
