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One advantage of approach (2) is that it allows one to discuss indeterminate forms in concrete fashion and distinguish several cases depending on the nature of numerator. Infinite numbers do exist in the hyperreal number system which properly extends the real number system, but then their reciprocals are infinitesimals rather than zero $\begingroup$ can this interpretation (subtract one infinity from another infinite quantity, that is twice large as the previous infinity) help us with things like.
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Infinite geometric series formula derivation When you replace each $\infty$ with any function/sequence whose limit is. Ask question asked 12 years, 2 months ago
Clearly every finite set is countable, but also some infinite sets are countable
Note that some places define countable as infinite and the above definition In such cases we say that finite. As far as i understand, the list of all natural numbers is countably infinite and the list of reals between 0 and 1 is uncountably infinite Cantor's diagonal proof shows how even a theoretically.
In the text i am referring for linear algebra , following definition for infinite dimensional vector space is given The vector space v(f) is said to be infinite dimensional. I know that $\sin(x)$ can be expressed as an infinite product, and i've seen proofs of it (e.g Infinite product of sine function)
I found how was euler able to create an infinite product for.
(the principal exception i know of is the extended hyperreal line, which has many infinite numbers obeying the 'usual' laws of arithmetic, and a pair of additional numbers we call $+\infty$ and $. Let us follow the convention that an expression with $\infty$ is defined (in the extended reals) if
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