class test one - until integration
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Injective | f(a)=f(b) implies a=b
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| Surjective | ∀b∈B ∃a∈A such that f(a)=b
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| Field | F, a non empty set with 2 binary operations + and . such that (F,+) is an abelian group with identity 0, (F\{0},.) is an abelian group with identity 1 and ∀a,b,c∈F a(b+c)=ab+ac
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| Ordered Field | relation < on F satisfying the following ∀a,b,c∈F
(i) with a<b, a=b, or b<a
(ii) a<b and b<c implies a<c
(iii) a<b implies a+c<b+c
(iv) a<b and 0<c implies ac<ab
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| Absolute Value | of every element of an ordered field
|x|= x if 0<x, -x if x<0, 0 if x=0
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| Completeness Axiom | for an ordered field F we say F is complete if F=A∪B such that A∩B=∅ and ∀a∈A, ∀b∈B
a<b implies ∃p∈F such that a≤p≤b
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| Archimedian Property | ∀a∈ℝ, ∃n∈ℕ, such that 0<(1/n)<a
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| Supremum | let ∅≠A⊆ℝ. sup(A)=s∈ℝ if
(i) ∀a∈A, a≤s
(ii) if ∃b∈ℝ such that ∀a∈A, a≤b then s≤b
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Created by:
meggle
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