(A remarkable discovery concerning a property of the natural numbers, both positive and negative.)
It is evident that the sum of the first n integers increases without bound as n increases without bound. Similarly the sum of first n negative numbers decreases without bound as n increases without bound. The positive and negative integers each, however, have but a single polarity, a one-sidedness that accounts for their forays into infinity, much as increasing a number of electrons increases a negative charge and increasing a number of positrons increases a positive charge.
However when we mix negative and positive charges the charges cancel each other, leaving an electrically neutral universe. The question, then, is whether the negative and positive integers similarly cancel each other out, or whether between them thre is a discrepancy favoring one polarity or the the other. Such is the case. Indeed we may arrange the summation of the positive and negative integers as follows:
1 + + (0 + 3 - 1 -2) + (2 + 5 - 3 -4) + (4 + 7 - 5 -6) + ... = 1 + 0 + 0 + 0 ... = 1It is likely that it is this remarkable discrepancy between the power of these two polarities that accounts for the domination of normal matter over anti-matter. As is well known, during the earliest period of the universe protons and anti-protons existed in great numbers, and then canceled each other out, leaving a slight residue of normal matter, just as the two infinities of positive and negative numbers cancel each other out, leaving a slight positive residue.
This page was last updated September 1, 2005.