Definite product of zero and infinity?

In summary, the conversation discusses the possibility of defining the product of zero and infinity as a finite quantity. It is mentioned that the differential calculus allows for the limit approach to zero while the integral calculus allows for the limit approach to infinity. However, the product of a quantity that tends to zero and one that tends to infinity may or may not have a limit. Examples are given to illustrate this, as well as a discussion on the validity of Boyle's law at extreme conditions. The concept of "zero pressure" and "infinite volume" is also debated. The conversation also delves into the concept of "near infinity" and "near zero" and the limits of mathematics when it comes to physical constraints. Ultimately, it is stated that the
  • #36
Thanks. I will start looking where I can get hold of this paper.
 
<h2> What does it mean for a product to be definite?</h2><p>A definite product is one that has a specific and unchanging value. It is not variable or uncertain, and can be calculated or determined with certainty.</p><h2> Can a product of zero and infinity be defined?</h2><p>No, a product of zero and infinity is considered to be indefinite because it does not have a specific value. It is a mathematical concept that cannot be accurately calculated.</p><h2> Why is a product of zero and infinity undefined?</h2><p>A product of zero and infinity is undefined because it leads to contradictory results. For example, if you multiply zero by any number, the result is always zero. However, if you multiply infinity by any number, the result is always infinity. Therefore, the product of zero and infinity cannot be determined.</p><h2> Can a product of zero and infinity be used in real-life situations?</h2><p>No, a product of zero and infinity is a theoretical concept and cannot be applied in real-life situations. It is often used in mathematics to explore the limits of certain equations, but it does not have practical applications.</p><h2> Are there any other mathematical operations that result in an indefinite product?</h2><p>Yes, division by zero also results in an indefinite product. This is because dividing any number by zero is undefined and leads to contradictory results. Therefore, both the product of zero and infinity and division by zero are considered indefinite in mathematics.</p>

FAQ: Definite product of zero and infinity?

What does it mean for a product to be definite?

A definite product is one that has a specific and unchanging value. It is not variable or uncertain, and can be calculated or determined with certainty.

Can a product of zero and infinity be defined?

No, a product of zero and infinity is considered to be indefinite because it does not have a specific value. It is a mathematical concept that cannot be accurately calculated.

Why is a product of zero and infinity undefined?

A product of zero and infinity is undefined because it leads to contradictory results. For example, if you multiply zero by any number, the result is always zero. However, if you multiply infinity by any number, the result is always infinity. Therefore, the product of zero and infinity cannot be determined.

Can a product of zero and infinity be used in real-life situations?

No, a product of zero and infinity is a theoretical concept and cannot be applied in real-life situations. It is often used in mathematics to explore the limits of certain equations, but it does not have practical applications.

Are there any other mathematical operations that result in an indefinite product?

Yes, division by zero also results in an indefinite product. This is because dividing any number by zero is undefined and leads to contradictory results. Therefore, both the product of zero and infinity and division by zero are considered indefinite in mathematics.

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