Newsletter 30: Friday 24 July 2026

Arithmetic Musings #17

Growth by multiplication. 

In Maths there several levels of intensity in the processes that expand or grow Number:

1. Counting upwards: 1, 2, 3, 4, ....
2. Addition: 3 + 5 = 8
3. Multiplication: 3 * 5 = 15
4. Powers; a base raised by an index: 2¹⁰ = 1,024; 10³ = 1,000
5. Integral Calculus: used to find the area under a curved line, or the sum of a series of numbers.

There appears to be no upper limit to the size of numbers, or perhaps we should it is undefined.  The term used for the largest number is Infinity. (without end, no finish)

It is interesting that the reverse processes that diminish or contract numbers come to thresholds and a new type of number is born, but you need to be attentive to notice rather than ignore it.

1. Counting downwards:  ....5, 4, 3, 2, 1, 0   zero, nothing, zilch, empty.  A new idea - but why be interested in nothing, haven't you got something to do?
2. Subtraction: 3 - 5 = -2,  Here there is confusion because the same symbol is used for quite different purposes: 

 z

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Over the next weeks, we will further some of the topics just mentioned here.  If you have any comments or requests, please feel free to contact me.  RB  robin@bacchus.co.nz