The Ring of Integers
... Definition. If x is a real number, then [x] denotes the greatest integer function of x. It is the largest integer less than or equal to x. It’s probably obvious to you based on your experience with the real numbers that there is such an integer [x]. You might find justifying this a bit of a challeng ...
... Definition. If x is a real number, then [x] denotes the greatest integer function of x. It is the largest integer less than or equal to x. It’s probably obvious to you based on your experience with the real numbers that there is such an integer [x]. You might find justifying this a bit of a challeng ...
TOPIC 1 Work with numbers
... 1 Find the number of significant figures in each number. a) 12.45 b) 0.0047 c) 50.06 d) 3.80 e) 5 000 2 Round each number correct to two significant figures. a) 4 315 b) 5 628 c) 73.02 d) 0.00876 e) 4.059 f) 5.1201 3 Round 3 510 228 as follows. a) The nearest 10 b) The nearest 100 c) The nearest 1 0 ...
... 1 Find the number of significant figures in each number. a) 12.45 b) 0.0047 c) 50.06 d) 3.80 e) 5 000 2 Round each number correct to two significant figures. a) 4 315 b) 5 628 c) 73.02 d) 0.00876 e) 4.059 f) 5.1201 3 Round 3 510 228 as follows. a) The nearest 10 b) The nearest 100 c) The nearest 1 0 ...
Here - Dartmouth Math Home
... • can 7 balls be placed in 4 boxes if no box is to be left empty? • can we give change of a pound? As suggested by the title of the course, we will be mainly concerned with counting problems, although on our way we will encounter algebraic and structural questions. The first thing we learn about mat ...
... • can 7 balls be placed in 4 boxes if no box is to be left empty? • can we give change of a pound? As suggested by the title of the course, we will be mainly concerned with counting problems, although on our way we will encounter algebraic and structural questions. The first thing we learn about mat ...
mathematics - Textbooks Online
... Sunday is the first day of the week. Wednesday is the ___________ day of the week. Friday is the _______________ day of the week. Saturday is the _____________ day of the week. January is the ________ month of the year. August is the __________ month of the year. The number of days in a week is _____ ...
... Sunday is the first day of the week. Wednesday is the ___________ day of the week. Friday is the _______________ day of the week. Saturday is the _____________ day of the week. January is the ________ month of the year. August is the __________ month of the year. The number of days in a week is _____ ...
31(2)
... First observe that, in any graph, two degree-one nodes having a common neighbor occur in the same Mis's. Thus, the number of Mis's is unaffected by the removal of one of these nodes. Such "pruning" can be repeated, and we formalize this fact as a lemma. Although the lemma is stated here for trees, i ...
... First observe that, in any graph, two degree-one nodes having a common neighbor occur in the same Mis's. Thus, the number of Mis's is unaffected by the removal of one of these nodes. Such "pruning" can be repeated, and we formalize this fact as a lemma. Although the lemma is stated here for trees, i ...
![1 How to Read and Do Proofs [1]](http://s1.studyres.com/store/data/007906654_1-0e74ecf2d08f104b19f4236120932fc3-300x300.png)
Propositional Statements Direct Proof
... a and b are said to have the same parity if both are even or both are odd. Proof: Given x, we have 2 options in life and x must be either odd or even. Case I: x is odd, so x = 2n + 1 for some n ∈ Z. We want x + 204 = 2m + 1 for some m ∈ Z x + 204 = 2n + 1 + 204 = 2n + 205 = 2(n + 102) + 1 ...
... a and b are said to have the same parity if both are even or both are odd. Proof: Given x, we have 2 options in life and x must be either odd or even. Case I: x is odd, so x = 2n + 1 for some n ∈ Z. We want x + 204 = 2m + 1 for some m ∈ Z x + 204 = 2n + 1 + 204 = 2n + 205 = 2(n + 102) + 1 ...
