lO JOURNAL OF THE 



finite number, however large; in other words, an infinite 

 number is a finite number! If such quantities have to be 

 considered they should be given a different name and sym- 

 bol to avoid confusing these with absolute infinity. The 

 letter G is suggested to distinguish such finite quantities 

 from absolute infinity oo. We get our ideas of infinity 

 from space and time, for finite as are our capacities, we 

 cannot conceive of space or time ever ending; hence we 

 speak of infinite space and infinite time. However far, in 

 imagination, one may travel in a straight line in space, it 

 is impossible to conceive of ever arriving at any point 

 where there is not infinite space beyond. The considera- 

 tion of a row of figures, loooo . . . , extended without 

 limit, gives one an idea of an itrfinite number. 

 Consider the quotient, 



a 



= .ooooi<ir, 



looooo- 

 where a is finite. 



The number of noughts in the right member is one less 

 than the number of noughts in the denominator, and suc- 

 cessive divisions by ten show that the same law holds, no 

 matter how great the denominator. 



If we conceive the number of noughts in the denominator 

 to be increased to several billion, the quotient is extremely 

 small, as in the right member we have the same number 

 of noughts less one before reaching the i ; thus as the 

 denominator increases indefinitely the value of the fraction 

 approaches zero indefinitely, and this is all that is meant 



a 

 bv the abbreviated notation, — = o. 



CO 



a 

 Similarly it may be shown, if — = y and .r decreases 



