sequences and series - What is the sum of an infinite resistor ladder ...
I am a little confused about how a cyclic group can be infinite. To provide an example, look at $\langle 1\rangle$ under the binary operation of addition. You can never make any negative numbers with
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.
Can you partition an infinite set, into an infinite number of infinite sets?
@foaly: "tensor product distributes over infinite direct products" is a question about the natural map being an isomorphism. Asking for there to be some arbitrary isomorphism is basically never the question you actually care about in practice.
Infinite summation formula for modified Bessel functions of first kind Ask Question Asked 7 years, 3 months ago Modified 1 year, 9 months ago
Login.gov This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Campus is an online college with professors who also teach at top universities. Explore our career focused associates degree and certificate programs.