The Summer Hill Journal Of New Physics

Ordinals and Quantities

Zero as an Ordinal number and as a Quantity

We can use zero as an integer for the purposes of counting. This is the case when we use zero as an ordinal value.

Examples where zero is an ordinal value:

• The set of integers { -2, -1, 0, 1, 2 }
• Powers of two: 2^-1, 2⁰, 2¹
• Latitude, longitude, other coordinates
• Computer software pointers and array indices.
• Hours : Minutes : Seconds on a digital clock

Zero as a null quantity

The conventions in mathematics generally assume that there is an answer to every operation, even division and multiplication. This is not the reality. If there is no input, there is no output.

We often don't cater for cases where a value is entirely missing and hence the result is null. In these instances we can use the null interpretation of zero: { } or a complete absence of any number.

Examples where zero may be a null quantity:

• Mass
• Energy
• Time
• Distance
• Money
• Apples

Zero as both

We sometimes use zero as both a quantity and an ordinal value in the same expression.

Example 1:

Zero is used as both a quantity and an ordinal number in:

00 (0^0 or zero raised to the 0th power).

Many have "proved" that 0⁰ = 1, generally of the basis that every non-zero number raised to the 0^th power equals 1, although opinion is divided. A null quantity cannot be raised to any power as there is nothing to raise, so the result is null.

Example 2:

In the number 10.01 the zeroes provide ordinal integer values between 9 and 1, but they also represent an absence of value (no units or tenths).

Also See

Rules on Ordinals and Quantities for more discussion on the difference "faces" of zero and why they require different rules.

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