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Imaginary Numbers

Name: !kuk54qxINg 2007-12-18 17:27

Are complex numbers any more imaginary than real numbers? What makes pi more real than i?

Name: Anonymous 2007-12-28 10:38

Any two real numbers that do not have at least one other number between them are equal.  Any number larger than 1 is also larger than .9999~repeating, and any number smaller than .9999~repeating is also smaller than 1.  So lets go for x such that x>.9999~repeating and x<1.  For X to be less than one, it has to have no nonzero digits to the left of the decimal point.  For X to be bigger than .9999~repeating, it has to follow the following condition:

Either the first decimal point we are considering has to be bigger than the number we are comparing it to, or equal to the number and repeat the test for the next digit over (this is easily deduced by changing this to the sum of 1/(10)^n terms).  For a number to be bigger than .9999~repeating, this implies that every single digit has to be 9, all the way to infinity... just like .9999~repeating is.

So there can't be another number between .9999~repeating and 1, so both numbers are equal.

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