Notes for 11th Jan (Wednesday)
... The previous proposition shows that indeed A has no largest number and B no smallest. Therefore, the rationals have gaps in between. The proposition also gives us an idea of how to correct them. Indeed, Definition : Let (S, ≤) be a totally ordered set (where a ≥ b means that b ≤ a). S is said to sa ...
... The previous proposition shows that indeed A has no largest number and B no smallest. Therefore, the rationals have gaps in between. The proposition also gives us an idea of how to correct them. Indeed, Definition : Let (S, ≤) be a totally ordered set (where a ≥ b means that b ≤ a). S is said to sa ...
Chapter 2: Integers & Introduction to Solving Equations
... To Add Two Numbers with Different Signs Step 1. Find the larger absolute value minus the smaller absolute value. Step 2. Use the sign of the number with the larger absolute value as the sign of the sum. Examples: ...
... To Add Two Numbers with Different Signs Step 1. Find the larger absolute value minus the smaller absolute value. Step 2. Use the sign of the number with the larger absolute value as the sign of the sum. Examples: ...
Proofs, Recursion and Analysis of Algorithms
... Assume that there is a finite number of primes. Let the value of s = the sum of all primes + 1. Therefore, s is not prime. Thus, s is composite and by the fundamental theorem of arithmetic, s can be factored as a product of (some of) the prime numbers. Suppose that pj is one of the prime factors of ...
... Assume that there is a finite number of primes. Let the value of s = the sum of all primes + 1. Therefore, s is not prime. Thus, s is composite and by the fundamental theorem of arithmetic, s can be factored as a product of (some of) the prime numbers. Suppose that pj is one of the prime factors of ...
class handout - English for Maths
... The most well-known constant is the ………………….which represents the number of diameters that fit in the ……………..of a circle. ...
... The most well-known constant is the ………………….which represents the number of diameters that fit in the ……………..of a circle. ...
Full text
... for each n>\. The recurrence in (3) is seen in a straightforward manner. Take a sequence of n (m- l)'s and r -l's that is counted by {?},„_,. The last element in the sequence is either a n m - 1 or a - 1 . If it is an m-1, then the preceding subsequence is one of those counted by {VL-i- On the other ...
... for each n>\. The recurrence in (3) is seen in a straightforward manner. Take a sequence of n (m- l)'s and r -l's that is counted by {?},„_,. The last element in the sequence is either a n m - 1 or a - 1 . If it is an m-1, then the preceding subsequence is one of those counted by {VL-i- On the other ...
