Thursday, January 05, 2012
Fractions & The Riemann Hypothesis
The Riemann Hypothesis involves an understanding of fractions . The largest fraction you can have is ( ½ ) or ( .5 ) . This may seem counter-intuitive, but to prove it simply subtract any fraction from ( ½ ) and you will end up with a positive fraction . The Riemann Hypothesis uses the formula ( 1 + ½ ^s + 1/3 ^s + ---- ) to infinity . In this formula you have ( s = ½ + it ) . You may be familiar with calculus , but if you aren't calculus is concerned with how close you can get to a fraction without actually touching ( reaching ) it . This getting close as a numerical figure is called a limit . You can think of it as how close you can get your nose to a brick wall without touching / hurting your nose . If you add fractions to infinity, you will find that the distance from ( ½ ) becomes smaller and smaller . If you add fractions to infinity that have been raised to a power, you will find that the distance from ( ½ ) is closer to ( ½ ) then by simply adding unraised fractions . Since the distance from ( ½ ) is getting closer, you can think of all the added fractions as getting closer to the line ( y = ½ ) . You may not know this, but if you raise a fraction to the power of zero ( 0 ), you get one ( 1 ) ( ½ ^0 = 1 ) . Zero ( 0 ) functions more as a placeholder than a value . Of course, you can argue that if you don't have anything you have something which is zero ( 0 ) . If the raised fraction to a power is getting closer and closer to ( ½ ), then the power to which it is being raised is getting closer and closer to zero ( 0 ) since ( ½ ) raised to the power of zero ( 0 ) is one ( 1 ) which means in the extreme ( ½ ) doesn't change because it becomes one or itself ( think philosophically here ) . One of the problems in mathematics is that you can't graph zero . You can, of course, draw a line and say this is line zero ( 0 ) meaning something you are considering starts here . If the power to which a fraction ( ½ ) is getting closer and closer to zero ( 0 ), then that zero ( 0 ) is getting closer and closer to ( ½ ) which is on the line ( y = ½ ) . Therefore it can be argued that zero ( 0 ) has the value of ( ½ ) on the line ( y = ½ ) . This is what Riemann said . The Riemann Hypothesis says that all the non-trivial zeros ( 0 ) are on the line ( y = ½ ) ( along with all the fractions added to ( ½ )).