Disputing 1 / 0 = Infinity: Agree or Disagree?

Thread starter zeromodz
Start date Feb 28, 2010
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Infinity

In summary, the conversation is discussing the concept of dividing by zero and whether the result is undefined or infinite. The majority agrees that the answer is undefined because infinity is not a number and cannot be reached. However, there is a debate on whether "approaches infinity" or "becomes infinite" is the correct terminology. Some argue that it depends on the number system being used and that in some systems, such as the Riemann sphere, 1/0 is equal to infinity. Ultimately, the disagreement stems from differing definitions and interpretations of infinity and how it relates to division by zero.

Mar 4, 2010

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

*sigh* By this point, I think any layperson who stumbles upon this thread is going to be more confused than helped, so I'm locking it.

If someone wants to start a thread on pedagogy, we can move over there and continue discussing that.

For the record, I'm not trying to be dogmatic here. I think much of the discussion has been reinforcing specific misunderstandings that people have about mathematics -- misunderstandings that the opening poster has even demonstrated!

<h2>1. What is the value of 1 divided by 0?</h2><p>The value of 1 divided by 0 is undefined. This means that there is no numerical answer to this division problem.</p><h2>2. Why is 1 divided by 0 considered undefined?</h2><p>This is because division by 0 leads to a mathematical contradiction. It violates the fundamental property of division which states that any number multiplied by 0 is equal to 0. Therefore, it is impossible to determine a value for 1 divided by 0.</p><h2>3. Can 1 divided by 0 be equal to infinity?</h2><p>No, 1 divided by 0 cannot be equal to infinity. Infinity is not a real number, it is a concept that represents a number that is larger than any other number. In mathematics, infinity is not considered a valid answer to a division problem.</p><h2>4. What is the concept of limits in mathematics and how does it relate to 1 divided by 0?</h2><p>Limits are used in mathematics to describe the behavior of a function as the input approaches a certain value. In the case of 1 divided by 0, the limit of the function is undefined. This means that as the input (denominator) approaches 0, the output (quotient) becomes larger and larger, but it does not reach a specific value.</p><h2>5. Is it possible for 1 divided by 0 to have a defined value in certain contexts?</h2><p>No, 1 divided by 0 will always be undefined regardless of the context. In some fields of mathematics, such as calculus, it is possible to define a concept called "extended real numbers" which includes an element called "infinity". However, this does not change the fact that 1 divided by 0 is undefined in the traditional sense of division.</p>

Related to Disputing 1 / 0 = Infinity: Agree or Disagree?

1. What is the value of 1 divided by 0?

The value of 1 divided by 0 is undefined. This means that there is no numerical answer to this division problem.

2. Why is 1 divided by 0 considered undefined?

This is because division by 0 leads to a mathematical contradiction. It violates the fundamental property of division which states that any number multiplied by 0 is equal to 0. Therefore, it is impossible to determine a value for 1 divided by 0.

3. Can 1 divided by 0 be equal to infinity?

No, 1 divided by 0 cannot be equal to infinity. Infinity is not a real number, it is a concept that represents a number that is larger than any other number. In mathematics, infinity is not considered a valid answer to a division problem.

4. What is the concept of limits in mathematics and how does it relate to 1 divided by 0?

Limits are used in mathematics to describe the behavior of a function as the input approaches a certain value. In the case of 1 divided by 0, the limit of the function is undefined. This means that as the input (denominator) approaches 0, the output (quotient) becomes larger and larger, but it does not reach a specific value.

5. Is it possible for 1 divided by 0 to have a defined value in certain contexts?

No, 1 divided by 0 will always be undefined regardless of the context. In some fields of mathematics, such as calculus, it is possible to define a concept called "extended real numbers" which includes an element called "infinity". However, this does not change the fact that 1 divided by 0 is undefined in the traditional sense of division.