modern mathematic an elementary apoproach1970 |
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Σελίδα 27
... proofs start in a variety of ways, but the following outline is usually typical. First of all, a proof starts with a known axiom, definition, or previously proved theorem, or with a combination of these. The problem of constructing the ...
... proofs start in a variety of ways, but the following outline is usually typical. First of all, a proof starts with a known axiom, definition, or previously proved theorem, or with a combination of these. The problem of constructing the ...
Σελίδα 28
... Proof: * + 3 = 5 Given (x +3) -3=5-3 Assumed axiom that one can subtract a number from both sides of an equality x + (3 - 3) =5- 3 Assumed axiom that one can group the 3-3 together x + 0 = 2 Subtraction x = 2 Addition of 0 These two ...
... Proof: * + 3 = 5 Given (x +3) -3=5-3 Assumed axiom that one can subtract a number from both sides of an equality x + (3 - 3) =5- 3 Assumed axiom that one can group the 3-3 together x + 0 = 2 Subtraction x = 2 Addition of 0 These two ...
Σελίδα 210
... Proof: We will divide the proof of this theorem into two parts. In the first part, we will show that every composite positive integer can be factored into primes. In the second part, it will be verified that the factorization is unique ...
... Proof: We will divide the proof of this theorem into two parts. In the first part, we will show that every composite positive integer can be factored into primes. In the second part, it will be verified that the factorization is unique ...
Περιεχόμενα
Sections 15 of Chapter | 3 |
Sets and Relations | 33 |
The System of Whole Numbers | 69 |
Πνευματικά δικαιώματα | |
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Additive identity additive inverse algorithm angles answer arithmetic mean Associative property Axiom called cartesian product Chapter Seven circle closed curve Commutative property concept congruent Consider counting numbers decimal defined Definition denoted digits discussion distributive property divide elements equation equivalent Exercise Set factors Figure Find Fractions and Rational frequency given greatest common divisor illustrated indicated inductive reasoning intersection irrational number least common multiple line segment mathematical system measure median mod 9 multiplicative inverse natural numbers number line numbers less Numeration Systems obtained one-to-one correspondence operation of addition ordered pairs plane polygon positive integer preceding prime numbers prism probability Proof property of addition property of multiplication prove rational numbers real numbers represent sample space set of points solution set square subset subtraction symbol system of integers system of whole Table Theorem Transitive property triangle true Venn diagrams verify whole numbers