Abstract Algebra
let a, b, c, d be integers. Prove the following statements: (a) if a|b and b|c. (b) if a|b and ac|bd. (c) if d|a and d|b then d|(xa+yb) for any x, y EZ
Big-O notation: If f(n) and g(n) are functions of a natural number n, we write f(n) is O(g(n)) and we say f is big-O of g if there is a constant C (independent of n) such that f
The Bolzano-Weierstrass property does not hold in C[0, ¶] for the infinite set A ={sinnx:n<N} : A is infinite; Show that has no “ limit points”.
For the demand function D(p)=410-0.2p(^2), find the maximum revenue.
II. Prove that Set Theory is a Model of a Boolean Algebra The three Boolean operations of Set Theory are the three set operations of union (U), intersection (upside down U), and complement ~. Addition is set
Prime number theorem: A big deal is known about the distribution of prime numbers and of the prime factors of a typical number. Most of the mathematics, although, is deep: while the results are often not too hard to state, the proofs are often diffic
The ABC Company, a merchandising firm, has budgeted its action for December according to the following information: • Sales at $560,000, all for cash. • The invoice cost for goods purc
integral e^(-t)*e^(tz) t between 0 and infinity for Re(z)<1
Wffs (Well-formed formulas): These are defined inductively by the following clauses: (i) If P is an n-ary predicate and t1, …, tn are terms, then P(t1, …, t
It's a problem set, they are attached. it's related to Sider's book which is "Logic to philosophy" I attached the book too. I need it on feb22 but feb23 still work
is the n-Dimensional Qn Hamiltonian? Prove tour answer
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