Would you be able to add to this list of known objects

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In summary, the conversation discusses the issue of confusing and muddled mathematical objects, and provides a list of distinct mathematical objects including points, lines, geometrical shapes, propositions, axioms, numbers, sets, elements, vectors, matrices, functions, derivatives, and integrals. The conversation also mentions the possibility of extending the list with more terms, and the importance of defining and clarifying terms in order to avoid ambiguity. One person also mentions their favorite mathematical concept, the Nilradical.
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Logical Dog
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So I was reading a book that warned me about mathematical objects and how they can be confused and muddled up for something else while being an entirely different thing..So, As far as I know these are distinct mathematical objects (which I think I know).

Is it a valid list and what are some that you may be able to add or correct?

1. Point.
2. Line.
3. Geometrical Shape
4. Proposition
5. Axiom,
6.Number
7.Set.
8. Element
9. Vector
10. Matrix
11. Function
12. Derivative (?)
13. Integral (?)
 
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A Boolean value (true or false).
 
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Bipolar Demon said:
So I was reading a book that warned me about mathematical objects and how they can be confused and muddled up for something else while being an entirely different thing..So, As far as I know these are distinct mathematical objects (which I think I know).

Is it a valid list and what are some that you may be able to add or correct?

1. Point.
2. Line.
3. Geometrical Shape
4. Proposition
5. Axiom,
6.Number
7.Set.
8. Element
9. Vector
10. Matrix
11. Function
12. Derivative (?)
13. Integral (?)

This list could probably be extended by at least some dozens of terms. The same is true for physics and likely many other sciences.
In addition it might depend on the language: something confusing in one language doesn't have to be confusing in another. E.g. integral domain is "integrity domain" in mine. That's why all used scientific terms are defined, before being used. Ordinary language is simply more restrictive than the range of scientific objects are, in the sense that it is ambiguous. This is already true by the normal usage without referring to science.
 
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Sometimes those words can be a burden: Just deleted a SPAM mail starting with "Save a bundle ..." and I was automatically thinking, why should I want to save a bundle ...
 

1. How do scientists identify known objects?

Scientists identify known objects through a variety of methods, such as observations, experimentation, and comparison with existing knowledge and data. They may also use specialized tools and techniques, such as telescopes or microscopes, to gather more information about the object.

2. What are some examples of known objects?

Known objects can range from microscopic organisms and cells to massive celestial bodies and galaxies. Some common examples of known objects include planets, stars, rocks, minerals, plants, animals, and man-made structures like buildings or bridges.

3. Can known objects change over time?

Yes, known objects can change over time due to natural processes or human intervention. For example, a rock can erode and change shape over time, or a plant can grow and change in appearance. Scientists continuously study known objects to track any changes and understand their causes.

4. How do scientists keep track of known objects?

Scientists keep track of known objects through various databases, catalogs, and records. They may also use scientific naming systems to classify and organize objects based on their characteristics and relationships. This allows for easier identification and comparison of known objects.

5. Why is it important for scientists to add to the list of known objects?

Adding to the list of known objects allows scientists to expand their understanding of the natural world and the universe. It also helps them make connections and discover patterns between different objects, leading to new discoveries and advancements in scientific knowledge.

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