Quote:
Originally Posted by sjastro
The correct term is countable and uncountable infinite sets.
A countable set is equivalent to the set of natural numbers N, if one can define a mapping function which is one-one and onto between the sets.
An infinite set that is not equivalent to N is uncountable.
Given that N is the common denominator in defining countable and uncountable sets you are wrong in asserting that mathematicians are using different conceptual frameworks involving infinity.
What has this got to do with the subject?
Do you seriously think that cosmologists have calculated the Universe as being infinite?
I suggest you try looking at http://en.wikipedia.org/wiki/Friedmann_equations.
Whether the Universe is infinite or not depends on the value of the curvature k used in the cosmological model under study.
What absolute hogwash.
Analytic continuation applies to analytic functions which are functions of the complex variable z.
Sorry to disappoint you but {1+2+3+4+....} are not complex numbers, they don't even form a power series on which analytical functions of both complex and real variables are based on.
As far as {1+2+3+4+.....} converging to -1/12 well I think any reasonably smart high school student will tell you otherwise.
I suspect Mr Polchinski is stating something very different.
Why don't you provide the relevant source.
Try reading the thread instead of cherry picking statements. |
Wow, you're response is very impressive.
Its strange that there are areas of Physics that actually use the result "Summation of positive integers, to infinity equaling -1/12"
If it's hogwash, then so are parts or all of String Theory (which is probably hogwash anyway)
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love cherries
