![arXiv:math/0412079v2 [math.NT] 2 Mar 2006](http://s1.studyres.com/store/data/013294887_1-d94fad656ee5fb5bde358f5c8c1d35cf-300x300.png)
Chapter 9: Transcendental Functions
... EXAMPLE 9.1.3 f = x2 and g = x1/2 are not inverses. While (x1/2 )2 = x, it is not true that (x2 )1/2 = x. For example, with x = −2, ((−2)2 )1/2 = 41/2 = 2. The problem in the previous example can be traced to the fact that there are two different numbers with square equal to 4. This turns out to be ...
... EXAMPLE 9.1.3 f = x2 and g = x1/2 are not inverses. While (x1/2 )2 = x, it is not true that (x2 )1/2 = x. For example, with x = −2, ((−2)2 )1/2 = 41/2 = 2. The problem in the previous example can be traced to the fact that there are two different numbers with square equal to 4. This turns out to be ...
rational number
... 3-1 Rational Numbers To write a finite decimal as a fraction, identify the place value of the farthest digit to the right. Then write all of the digits after the decimal points as the numerator with the place value as the denominator. ...
... 3-1 Rational Numbers To write a finite decimal as a fraction, identify the place value of the farthest digit to the right. Then write all of the digits after the decimal points as the numerator with the place value as the denominator. ...
Nonnegative k-sums, fractional covers, and probability of small
... this hypergraph does not have a perfect k-matching. One can prove there are at least n−1 k−1 edges in the complement of such a hypergraph, which exactly tells the minimum number of nonnegative ksums. We utilize the same idea to estimate the number of nonnegative k-sums involving x1 . Construct a (k ...
... this hypergraph does not have a perfect k-matching. One can prove there are at least n−1 k−1 edges in the complement of such a hypergraph, which exactly tells the minimum number of nonnegative ksums. We utilize the same idea to estimate the number of nonnegative k-sums involving x1 . Construct a (k ...
7.4c student activity #1
... Use the ______________ __________________ to find a pattern that shows the relationship between a term’s _______________ number and the _______________ of the term. The common difference is _____. _______________ the common difference times the position number in the sequence. _____ _____ = _____ ...
... Use the ______________ __________________ to find a pattern that shows the relationship between a term’s _______________ number and the _______________ of the term. The common difference is _____. _______________ the common difference times the position number in the sequence. _____ _____ = _____ ...
Algebraic Proofs - GREEN 1. Prove that the sum of any odd number
... Prove that the sum of any odd number and any even number is odd. Prove that half the sum of four consecutive numbers is odd. Prove that the sum of any three consecutive numbers is a multiple of 3. Prove that the product of any odd number and any even number is even. Prove that the product of any two ...
... Prove that the sum of any odd number and any even number is odd. Prove that half the sum of four consecutive numbers is odd. Prove that the sum of any three consecutive numbers is a multiple of 3. Prove that the product of any odd number and any even number is even. Prove that the product of any two ...
Rational and Irrational Numbers
... from just the infinite set of rational numbers, after all between any two rational numbers we can always find another. It took mathematicians hundreds of years to show that the majority of Real Numbers are in fact irrational. The rationals and irrationals are needed together in order to complete the ...
... from just the infinite set of rational numbers, after all between any two rational numbers we can always find another. It took mathematicians hundreds of years to show that the majority of Real Numbers are in fact irrational. The rationals and irrationals are needed together in order to complete the ...
CMSC 203 / 0202 Fall 2002
... Theorem. If f and fg are one-to-one, then g is one-to-one. Proof. Suppose that g is not one-to-one. Then (by the definition of “one-to-one”) there must exist some values w and z in the domain of g such that g(w) = g(z) and w < > z. But since g(w) = g(z), it must be the case that f(g(w)) = f(g(z ...
... Theorem. If f and fg are one-to-one, then g is one-to-one. Proof. Suppose that g is not one-to-one. Then (by the definition of “one-to-one”) there must exist some values w and z in the domain of g such that g(w) = g(z) and w < > z. But since g(w) = g(z), it must be the case that f(g(w)) = f(g(z ...