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What is Xeno's Paradox

Xeno's paradox refers to a basic calculus II problem in dealing with infinite series and sequences. The Greek symbol sigma, that weird E thats kinda bent in the middle is a summation relation. The number under the symbol is the starting phrase of your variables initial value and the top number is where it will stop so [{2/E/x=1} x] means 3, x starts at one and ends at 2 and all of the numbers in the sequence are added. Now that the basics are kinda covered you can look at different forms such as placing infinity on top of the E. If the sequence will infinitely add numbers then how can we possibly know the value of the equation? this is where convergence and divergence enter the realm. If the equation 'Diverges' then it drifts off to infinity, but if it converges then we may find an actual value. take for instance [{infinity/E/x=1} x] thus every number from 1 to infinity is added, this diverges because there is no real value to obtain because every number up to infinity including infinity added will give you infinity and there the math gets a little too scary for here and now so we just say it diverges. Now if we have [{infinity/E/x=1) 1/x] then we will add 1+ 1/2 + 1/3 + 1/4 and there is a definite decay in the value added so we may not reach infinity, unfortunately 1/x is a p series equation that actually does diverge thought 1/(x^2) is convergent. now lets look at a simpler one that relates to Xeno's paradox. [ {infinity/E/x=1} {1/(2^x)} ] thus we will have 1/2+1/4+1/8+1/16+..... where on each iteration we halve the amount between the current sum and 1 getting infinitely closer and closer to 1 but never in fact reaching it, this is called converging to 1. If we had [ {infinity/E/x=1} {2/(2^x)} ] then we would converge at 2 because its 1+1/2+1/4+1/8+........

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