sequences and series - What is the sum of an infinite resistor ladder ...
This resolves your problem because it shows that $\frac {1} {\epsilon}$ will be positive infinity or infinite infinity depending on the sign of the original infinitesimal, while division by zero is still undefined. This viewpoint helps account for all indeterminate forms as well, such as $\frac {0} {0}$.
If the vector space is finite dimensional, then it is a countable set; but there are infinite-dimensional vector spaces over $\mathbb {Q}$ that are countable as sets.
I would like to have some examples of infinite dimensional vector spaces that help me to break my habit of thinking of $\mathbb{R}^n$ when thinking about vector spaces.
There is an easier way to determine whether a system of equations has unique, infinite or no solution. It is as follows: calculate determinant $D$ of the coefficients of the three variables in three equations, then calculate $Dx$, where the x coefficients with the constant terms in the determinant $D$.
Set of Linear equation has no solution or unique solution or infinite ...
Can you partition an infinite set, into an infinite number of infinite sets?
It's certainly true that there is no universal algorithm for solving such problems. But quite universal method of showing that a group is infinite (or non-trivial) is constructing transitive action on infinite (resp. non-trivial) set.
How do you prove that a group specified by a presentation is infinite ...
2 Consider a sphere of infinite radius, with a hole of radius R cut in it. The interior or exterior surface has infinite area, but the bounding edge has a finite length of the circumference of the hole...