algebra precalculus
@Arturo: I heartily disagree with your first sentence. Here''s why: There''s the binomial theorem (which you find too weak), and there''s power series and polynomials (see also Gadi''s answer). For all this,
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Zero power zero and $L^0$ norm
This definition of the "0-norm" isn''t very useful because (1) it doesn''t satisfy the properties of a norm and (2) $0^ {0}$ is conventionally defined to be 1.
factorial
The product of 0 and anything is $0$, and seems like it would be reasonable to assume that $0! = 0$. I''m perplexed as to why I have to account for this condition in my factorial function (Trying to learn
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What is $0^ {i}$?
In the context of natural numbers and finite combinatorics it is generally safe to adopt a convention that $0^0=1$. Extending this to a complex arithmetic context is fraught with risks, as is
Why does 0.00 have zero significant figures and why throw out the
A value of "0" doesn''t tell the reader that we actually do know that the value is < 0.1. Would we not want to report it as 0.00? And if so, why wouldn''t we also say that it has 2 significant
What exactly is a 0-form?
A $0$-form on a vector space is just a scalar. A $0$-form on a manifold is a function (i.e. it assigns a scalar to each tangent space of the manifold).
Breakdown of Solar Pv System Costs by Market Segment
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Why is 0 factorial equal to 1? Is there any pure basic mathematical
$$ 0! = Gamma (1) = int_0^ {infty} e^ {-x} dx = 1 $$ If you are starting from the "usual" definition of the factorial, in my opinion it is best to take the statement $0! = 1$ as a part of the
Is $0$ a natural number?
Inclusion of $0$ in the natural numbers is a definition for them that first occurred in the 19th century. The Peano Axioms for natural numbers take $0$ to be one though, so if you are working with these
definition
If you take the more general case of lim x^y as x,y -> 0 then the result depends on exactly how x and y both -> 0. Defining 0^0 as lim x^x is an arbitrary choice. There are unavoidable
I have learned that 1/0 is infinity, why isn''t it minus infinity?
@Swivel But 0 does equal -0. Even under IEEE-754. The only reason IEEE-754 makes a distinction between +0 and -0 at all is because of underflow, and for +/- ∞, overflow. The intention is if you have