Newsletter 19: Sunday 10 May 2026

Click on the link for last week's musings.

This week's theme:   

Number Sets and Negativity

For millennia, numbers were just “counting numbers” which today we call the SET of Natural Numbers (ℕ) 

A set of Natural numbers (or counting numbers) includes all positive numbers without fractions or decimals that start from 1 and continue indefinitely { …} – without end. 

In mathematical symbols:  ℕ = {1, 2, 3, 4, …}

Counting up is a form of expansion – getting bigger and bigger, unlimited.

Counting down is a form of contraction – getting smaller and smaller – but not without end.  We come to a threshold, a limit, when we get down to 1, we cannot go any further, we have run out of numbers.

 To break through this threshold we have to be creative, to create a new number – that is zero, 0, the empty basket, nothingness!  You might say, in very early times people did not see any point in counting nothing, that is something that wasn’t there.  However, mathematicians and philosophers did ponder these things: “And the earth was without form, and void.”  It was just an idea in the mind of the Creator God, not yet manifest physically.

Here are some ways that early civilisations represented the idea of “nothingness”, an empty gap between:

I wonder if the Mayan symbol represents a closed eye – when our eyes are closed we see nothing!

Anyway, the acceptance of zero leads to a new, greater set of numbers, namely:

Whole Numbers ('')

 A set of Whole numbers consists of all natural numbers, including 0. 

That is: '' = {0, 1, 2, 3, 4, …}

If ‘nothing’ is a problem for people to accept, then ‘less than nothing’ is going to be much harder to accept.

If you have a basket of apples and you have given away all the apples that you have in the basket, how can you give away any more? …give away what you don’t have?
You could, however, give a promise!  A promise of future action.  Such a promise, your word, is an obligation, like a debt!

When you have something, it is a fortune, an asset; when you have promised something to someone, it is an obligation, a debt to be taken from what you may acquire in the future.

It is an interesting gesture – to give away what you do not yet have.  Is that Generosity, Foolishness, or Fraud?
Let us explore the polarity warm <> cool further:

Add, plus, acquiring, selfishness <<<  >>>  Subtract, minus, giving, altruism.

Words are often coloured with feelings - these related polar words reflect that in a different way:

               Asset                  Debt
               Positive             Negative
               Good                  Bad, evil

Where can we experience “less than nothing” in daily life? 

With money! 

Money is an idea, a belief.  

I believe that the currency, the notes and coins in my purse have value – that they are tokens for value.  We are continually making equations, comparisons:  The value of an object (that I wish to purchase) to me compared to the value of the monetary token to me. 

Only when they are equal (or better) will I make a purchase.

Value of object = Value of money.   

This ‘equals’ symbol =, comes from the Scales [the 7^th sign of the zodiac is Libra – Scales; Hips in the human body – keeping balance as we walk] or the mechanical Balance we use for weighing things, that is comparing an object’s weight with standard weights – pounds and ounces, or kilograms and grams.  (In England, for many years the same word, ‘pound’, was used to name a unit of weight and a unit of money!)

The derivation of comparison symbols:

7 > 5, so the difference is positive: 7 - 5 = 2

7 < 9, so the difference is negative:  7 - 9 = -2, a number below zero, 0.

Unfortunately the same symbol, -, is often used for both the operation of subtraction and the position of a number below zero.  This can lead to confusion - more about this in a future musing.

Where else is the idea of ‘negative’ numbers used, at least partially?

In historical time - for dates before a key event, such as the birth of Jesus Christ [BC] [but note there is no Year 0 between BC and AD or CE].

In a building: positive numbers for the floor levels above ground; negative for the basement floors below ground level.

So we come to the next set of numbers:

Integers (ℤ)

A set of integers includes all positive and negative natural numbers and zero. 

Example

ℤ = {…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …}

Some more next week.

Robin