Rational and Irrational Numbers - School of Computer Science
... That is, for any number ǫ > 0, we can find a rational number r whose difference from z is less than ǫ. In fact, we can show that any irrational (and non-”complex”) number can be expressed as a decimal number with infinitely many digits after the decimal point (where the digits after the point never ...
... That is, for any number ǫ > 0, we can find a rational number r whose difference from z is less than ǫ. In fact, we can show that any irrational (and non-”complex”) number can be expressed as a decimal number with infinitely many digits after the decimal point (where the digits after the point never ...
Set theory
... A set is infinite if and only if it has the same size as some proper subset Two arbitrary sets M and N (finite or infinite) are said to be of equal size or cardinality, if and only if there exists a bijection from M onto N. Set M countable if it can be put in one-to-one correspondence with N ...
... A set is infinite if and only if it has the same size as some proper subset Two arbitrary sets M and N (finite or infinite) are said to be of equal size or cardinality, if and only if there exists a bijection from M onto N. Set M countable if it can be put in one-to-one correspondence with N ...
CS103X: Discrete Structures Homework Assignment 5
... Exercise 4 (10 points). Prove that if every point on a line is painted cardinal or white, there exists three points of the same color such that one is the midpoint of the line segment formed by the other two. Solution Pick two points A, B of the same color. Let C be the midpoint of AB, and position ...
... Exercise 4 (10 points). Prove that if every point on a line is painted cardinal or white, there exists three points of the same color such that one is the midpoint of the line segment formed by the other two. Solution Pick two points A, B of the same color. Let C be the midpoint of AB, and position ...
Powerpoint - introduction to the basics
... A spreadsheet is used for storing information and data. Calculations can be performed on the data in a spreadsheet. Microsoft Excel is the most common spreadsheet application, although there are other spreadsheets available. ...
... A spreadsheet is used for storing information and data. Calculations can be performed on the data in a spreadsheet. Microsoft Excel is the most common spreadsheet application, although there are other spreadsheets available. ...
Algebra Review 2 - Amherst College
... one might make to one side of an equation, usually in an effort to isolate a variable or to isolate all terms containing that variable – and scalar terms, which contain x0: adding a quantity, subtracting a quantity, multiplying by a quantity, dividing by a quantity, squaring, cubing, finding the squ ...
... one might make to one side of an equation, usually in an effort to isolate a variable or to isolate all terms containing that variable – and scalar terms, which contain x0: adding a quantity, subtracting a quantity, multiplying by a quantity, dividing by a quantity, squaring, cubing, finding the squ ...
Prime and Composite Numbers
... 3. Only the natural numbers greater than or equal to 2 are considered prime or composite. 4. One is neither prime nor composite. By definition, a prime number must have exactly two factors. Since 1 has only one factor, 1, it does not meet the definition of a prime number. Since all composite numbers ...
... 3. Only the natural numbers greater than or equal to 2 are considered prime or composite. 4. One is neither prime nor composite. By definition, a prime number must have exactly two factors. Since 1 has only one factor, 1, it does not meet the definition of a prime number. Since all composite numbers ...
