Is there a named axiom for this?

• 1MileCrash
In summary, the absolute difference between any two naturals/rationals/reals/complex; is also a natural/rational/real/complex. This concept is also known as the closure axiom in abstract algebra.
1MileCrash
"The absolute difference between any two naturals/rationals/reals/complex; is also a natural/rational/real/complex."

This should be fairly intuitive but I was wondering if there was a name for this.

1MileCrash said:
"The absolute difference between any two naturals/rationals/reals/complex; is also a natural/rational/real/complex."

This should be fairly intuitive but I was wondering if there was a name for this.

In abstract algebra, they define an operation of addition and define inverses with the statement that adding any two elements produces another element in the ring. These are considered the axioms of the ring.

http://en.wikipedia.org/wiki/Ring_(mathematics )

I think its called the closure axiom.

http://en.wikipedia.org/wiki/Axiom_of_closure

Last edited by a moderator:
Thank you.

1. Is there a named axiom for this?

The answer to this question depends on what specific axiom you are referring to. There are many different axioms in various fields of science, such as mathematics, physics, and biology. It would be helpful to specify which axiom you are asking about.

2. What is the purpose of having named axioms?

The purpose of having named axioms is to provide a clear and concise statement of a fundamental principle or concept in a particular field of science. These named axioms serve as starting points for building theories and models, and they help to establish a common language and understanding among scientists.

3. How are named axioms determined and named?

Named axioms are typically determined through observation, experimentation, and analysis in a specific field of science. The naming of an axiom may vary depending on the culture and language of the scientists involved, but it is often named after the scientist who first proposed it or after a key concept or principle it represents.

4. Can named axioms be disproven or changed?

Yes, named axioms can be disproven or changed if new evidence or discoveries challenge their validity. Science is constantly evolving, and axioms are subject to revision as our understanding of the natural world expands and improves.

5. Are named axioms universally accepted in the scientific community?

No, not all named axioms are universally accepted in the scientific community. Some may be considered controversial or debated among scientists, and may even be rejected if they are not supported by sufficient evidence or do not fit with current theories and models. However, most named axioms are widely accepted and considered fundamental principles in their respective fields of science.

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