Possible to Multiply or Divide Infinities?

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In summary, the conversation discussed the concept of infinity and whether it is possible to perform arithmetic operations on it. Some argued that it is possible to divide, multiply, add, and subtract infinities, while others believed it was impossible. However, it was acknowledged that infinity is not a number and therefore, traditional arithmetic operations do not apply to it. The conversation also mentioned the use of the Dirac delta function in evaluating multiple integrals in Quantum Field Theory and the different meanings one can assign to the words "divide", "multiply", "add", "subtract", and "infinity". It was also noted that arithmetic operations on infinite sets can differ for regular and singular cardinals.
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Also, in your former definition, 0/anything = class of all cardinals. While in the latter 0/anything = 0.
 
<h2>1. Can infinity be multiplied or divided?</h2><p>Yes, infinity can be multiplied or divided in certain mathematical contexts. However, it is important to note that infinity is not a number and does not follow the same rules as finite numbers.</p><h2>2. What is the result of multiplying infinity by infinity?</h2><p>The result of multiplying infinity by infinity is undefined. This is because there are different types of infinity, and some infinities are larger than others.</p><h2>3. Is it possible to divide infinity by infinity?</h2><p>Yes, it is possible to divide infinity by infinity in certain mathematical contexts. However, the result of this division is also undefined.</p><h2>4. Can infinity be divided by a finite number?</h2><p>Yes, infinity can be divided by a finite number. The result of this division is infinity, as any finite number becomes insignificant when compared to infinity.</p><h2>5. Is there a largest or smallest infinity?</h2><p>No, there is no largest or smallest infinity. In mathematics, there are different types of infinity, each with its own properties and size. Therefore, there is no single infinity that can be considered the largest or smallest.</p>

FAQ: Possible to Multiply or Divide Infinities?

1. Can infinity be multiplied or divided?

Yes, infinity can be multiplied or divided in certain mathematical contexts. However, it is important to note that infinity is not a number and does not follow the same rules as finite numbers.

2. What is the result of multiplying infinity by infinity?

The result of multiplying infinity by infinity is undefined. This is because there are different types of infinity, and some infinities are larger than others.

3. Is it possible to divide infinity by infinity?

Yes, it is possible to divide infinity by infinity in certain mathematical contexts. However, the result of this division is also undefined.

4. Can infinity be divided by a finite number?

Yes, infinity can be divided by a finite number. The result of this division is infinity, as any finite number becomes insignificant when compared to infinity.

5. Is there a largest or smallest infinity?

No, there is no largest or smallest infinity. In mathematics, there are different types of infinity, each with its own properties and size. Therefore, there is no single infinity that can be considered the largest or smallest.

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