- #1

Willelm

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By mathematical context, is there something undifined by mathematics?

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- Thread starter Willelm
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In summary, the conversation discusses the concept of something being undefined in mathematics. Gödel's theorem states that there are true statements that cannot be proved and false statements that cannot be disproved in pure mathematics. However, mathematics is a tool to describe real-world phenomena and it is not clear what is meant by "undefined by mathematics". It is mentioned that any number divided by zero is undefined, and in mathematics or logic, statements are only defined if they are well-formed formulae. Therefore, any statement that is not a well-formed formula is considered undefined.

- #1

Willelm

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By mathematical context, is there something undifined by mathematics?

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- #2

Svein

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Sure. If you are talking pure mathematics, Gödels famous theorem states that there are some true statements that cannot be proved (and some false statements that cannot be disproved).Willelm said:By mathematical context, is there something undifined by mathematics?

So what? Mathematics isn't physics - or chemistry or... Mathematics is a tool to help you describe some real-world phenomena.

- #3

HallsofIvy

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- #4

newjerseyrunner

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1/0 is undefined.

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Brian Olson

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Any number divided by zero is undefined.newjerseyrunner said:1/0 is undefined.

- #6

TeethWhitener

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More to the point, statements in mathematics or logic are only defined if they areHallsofIvy said:As Svein said, given any axiom system there exist statements that can be phrased in that system but neither proven nor disproven. But you said "undefined", not "proved".

Currently, there is no scientific evidence to support the existence of any object or phenomenon that is considered "antimathematical." Mathematics is a fundamental part of the laws governing the universe, and all observable phenomena can be described and predicted using mathematical principles.

Yes, mathematical concepts can be applied to non-mathematical objects or systems. This is often done in fields such as physics, where mathematical models are used to describe and understand the behavior of physical systems.

No, there are no known examples of objects that defy mathematical principles. While there may be phenomena that are difficult to explain or understand using current mathematical theories, there is no evidence to suggest that any object or system operates outside of mathematical principles.

Yes, mathematics can be used to study abstract concepts or ideas. In fact, mathematics is often used to explore and understand abstract concepts, such as infinity, symmetry, and higher dimensions.

Yes, it is possible for a mathematical concept or theory to be proven wrong or invalid. Mathematics is an ever-evolving field, and new discoveries and advancements can sometimes lead to the rejection or revision of previously accepted theories. However, this does not mean that the entire field of mathematics is incorrect or unreliable.

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