Chapter 5: Rational Numbers
... 43. Express two hundred and nineteen hundredths as a fraction or mixed number in simplest form. Determine whether each statement is sometimes, always, or never true. Explain by giving an example or a counterexample. 44. An integer is a rational number. 45. A rational number is an integer. 46. A whol ...
... 43. Express two hundred and nineteen hundredths as a fraction or mixed number in simplest form. Determine whether each statement is sometimes, always, or never true. Explain by giving an example or a counterexample. 44. An integer is a rational number. 45. A rational number is an integer. 46. A whol ...
Integers - Big Ideas Math
... a. Describe the pattern in the table. How many feet do the balloons move each second? After how many seconds will the balloons be at a height of 40 feet? b. What integer represents the speed of the balloons? Give the units. c. Do you think the velocity of the balloons should be represented by a posi ...
... a. Describe the pattern in the table. How many feet do the balloons move each second? After how many seconds will the balloons be at a height of 40 feet? b. What integer represents the speed of the balloons? Give the units. c. Do you think the velocity of the balloons should be represented by a posi ...
NSCC SUMMER LEARNING SESSIONS NUMERACY SESSION
... All signed numbers have magnitude (i.e. how far you move to the right or left) and direction (i.e. sign: positive - move to right, negative - move to left). • For example, the number -4 has a negative direction (to the left of 0 on the number line) and a magnitude of 4. • For example, the number -3. ...
... All signed numbers have magnitude (i.e. how far you move to the right or left) and direction (i.e. sign: positive - move to right, negative - move to left). • For example, the number -4 has a negative direction (to the left of 0 on the number line) and a magnitude of 4. • For example, the number -3. ...
Sequences of Numbers Involved in Unsolved Problems, Hexis, 1990, 2006
... also online, email: [email protected] ( SUPERSEEKER by N. J. A. Sloane, S. Plouffe, B. Salvy, ATT Bell Labs, Murray Hill, NJ 07974, USA); N. J. A. Sloane, e-mails to R. Muller, February 13 - March 7, 1995. ...
... also online, email: [email protected] ( SUPERSEEKER by N. J. A. Sloane, S. Plouffe, B. Salvy, ATT Bell Labs, Murray Hill, NJ 07974, USA); N. J. A. Sloane, e-mails to R. Muller, February 13 - March 7, 1995. ...
On the Classification of Integral Quadratic Forms
... We are concerned with the classification of integral quadratic forms under integral equivalence. There are two definitions of integrality for a quadratic form. The binary form (2) is integral as a quadratic form if a, 2b and c belong to Z, and integral as a symmetric bilinear form if its matrix entr ...
... We are concerned with the classification of integral quadratic forms under integral equivalence. There are two definitions of integrality for a quadratic form. The binary form (2) is integral as a quadratic form if a, 2b and c belong to Z, and integral as a symmetric bilinear form if its matrix entr ...
P-adic number
In mathematics the p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number systems. The extension is achieved by an alternative interpretation of the concept of ""closeness"" or absolute value. In particular, p-adic numbers have the interesting property that they are said to be close when their difference is divisible by a high power of p – the higher the power the closer they are. This property enables p-adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles.p-adic numbers were first described by Kurt Hensel in 1897, though with hindsight some of Kummer's earlier work can be interpreted as implicitly using p-adic numbers. The p-adic numbers were motivated primarily by an attempt to bring the ideas and techniques of power series methods into number theory. Their influence now extends far beyond this. For example, the field of p-adic analysis essentially provides an alternative form of calculus.More formally, for a given prime p, the field Qp of p-adic numbers is a completion of the rational numbers. The field Qp is also given a topology derived from a metric, which is itself derived from the p-adic order, an alternative valuation on the rational numbers. This metric space is complete in the sense that every Cauchy sequence converges to a point in Qp. This is what allows the development of calculus on Qp, and it is the interaction of this analytic and algebraic structure which gives the p-adic number systems their power and utility.The p in p-adic is a variable and may be replaced with a prime (yielding, for instance, ""the 2-adic numbers"") or another placeholder variable (for expressions such as ""the ℓ-adic numbers""). The ""adic"" of ""p-adic"" comes from the ending found in words such as dyadic or triadic, and the p means a prime number.