RE: Is zero a natural number?
May 20, 2023 at 2:11 am
(This post was last modified: May 20, 2023 at 4:00 am by Carl Hickey.)
Hi,
Let's take a set of apples.
The set is full. If there were no apples the the set would be empty.
Full set and empty set are complementary.
Let's state that a quality of a full set is a Natural number.
- - -
An unoriented line segment (1 d) is a set of units (Greeks, rational numbers (set (of sets (of ...))).
Rational numbers are natural numbers. Greeks discovered irrational numbers (square root of 2).
Irrational numbers are not natural numbers (not expressed as set (of sets)).
= = =
empty (zero)
full:
- unoriented (0 d, set (natural number))
- oriented line segment (1 d, vector);
- oriented piece of plane (2 d, bi-vector);
- oriented volume (3 d, ...);
- ...
= = =
...
Let's take a set of apples.
The set is full. If there were no apples the the set would be empty.
Full set and empty set are complementary.
Let's state that a quality of a full set is a Natural number.
- - -
An unoriented line segment (1 d) is a set of units (Greeks, rational numbers (set (of sets (of ...))).
Rational numbers are natural numbers. Greeks discovered irrational numbers (square root of 2).
Irrational numbers are not natural numbers (not expressed as set (of sets)).
= = =
empty (zero)
full:
- unoriented (0 d, set (natural number))
- oriented line segment (1 d, vector);
- oriented piece of plane (2 d, bi-vector);
- oriented volume (3 d, ...);
- ...
= = =
...