The Axiom of Infinity is the fourth of the first four axioms in my system of ten axioms based on the ways of figuring things out.
Thoughts about infinity
- Tools for solving math are all based on finite thinking (except for continuity arguments, etc.) not using the Axiom of Infinity. But the objects of study in mathematics are all essentially infinite - "general" - for example there are infinitely many integers, there are infinitely many values a variable may take, there are infinitely many solutions to the Pythagorean theorem, etc. Generally, mathematical statements (with a free variable) apply to infinitely many (non finite, nonrestricted) situations. That is why infinitary disjunctions are allowed (infinitely many things) but only finitary conjunctions (finite combinations). By analogy, this is how the conscious mind rules the unconscious mind, or how the small ordering orders the large ordering in a visualization.