Infinitely large times the infinitesimally small

[Dale]

IEEE floating point contains two signed infinities and is algebraicly complete. Although I have not been able to Google up an explicit statement, this strongly implies that $\frac{1}{+\text{inf}}$ yields a result of 0.

Note, however, that IEEE floating point is not an algebraic field. It has behaviors that violate other axioms that the real numbers (for instance) adhere to.

So when I asked the OP what $\infty$ is then one reasonable response would have been that it is the IEEE floating point signed infinity. And if you are right then the statement would be true there.

But then the problem is that the question in the OP cannot be asked because there is no infinitesimal number in the IEEE floating point.

 

[Hornbein]

Mentor note: changed the thread title so readers don't mistake this for a question about verb forms.
What is result of infinitive times infinitive small?
Infinitive?

Rearrange A*B to A/(1/B) then try L'Hopital's Rule.

 

[sophiecentaur]

IEEE floating point contains two signed infinities and is algebraicly complete. Although I have not been able to Google up an explicit statement, this strongly implies that $\frac{1}{+\text{inf}}$ yields a result of 0.

Note, however, that IEEE floating point is not an algebraic field. It has behaviors that violate other axioms that the real numbers (for instance) adhere to.

This is really all a bit of a non-sequiter The set of numbers used in floating point arithmetic is defined to deal with values that are encountered in 'real' life. in my Maths Analysis course we were told to be scrupulous about open and closed intervals and the use of continuous and differentiable.

To get this properly sorted out, you need to go much deeper into 'proper' Maths. You can't rxpect a group of Engineers to come up with a working rule that behaves itself outside the range of experience. The term +inf is pragmatic. Without it, they. would still be arguing about what zero and infinity mean. That's the job of Mathematicians. The concept of the limit is not too hard to get on top of and it gets you through a lot of Maths but there are many processes that can't be dealt with so simply.