Flashcards
Theorems
Cards in this deck (33)
- 1Closure1. Take any 2 elements of a set
2. Perform a binary operation on them
3. If your answer is always an element of the original set, then you have a closure - 2GroupingWhenever you take off or put on symbols of inclusion
( ) { } [ ] - 3RThe set of real numbers
- 4AxiomsA statement that you can assume to be true
- 5Comm (x)ab=ba
- 6Comm (+)a+b=b+a
- 7Assoc (+)a+(b+c)=(a+b)+c
- 8Assoc (x)a(bc)=(ab)c
- 9Reflexivea=a
- 10SymmetryIf a=b then b=a
- 11TransitiveIf a=b and b=c, then a=c
- 12SubstitutionWhenever you take something out and replace it with something of equal value
- 13. . .Therefore
- 14Theorems1. Statements that must be proven
2. Once you prove a theorem, you may use it to prove a later theorem - 15LHDa(b+c)=ab+ac
- 16Id (+)a+0=a
- 17Inv (+)a+ (-a)=0
- 18==>Implies
- 19<==>If and only if
- 20/"Not"
- 21Inv (x)a (1/a)
a does not equal 0 - 22Id (x)a (1)=a
- 23Thm 6a0=0
- 24Deft Subta-b=a+(-b)
- 25Def Expa^2= aa
a^3= aaa
a^4= aaaa - 26Def Divb is not equal to zero
a/b=a (1/b) - 27Proof by Contradiction1. Assume the conclusion is false
2. Show a contradiction to the given, a definition, axiom, previous theorem, or other known fact - 28Lemma1. A theorem needed to prove the main theorem
2. A fact that you want to use that has not been proven yet - 29Defn Ordera b>a
- 30Trichotomyab or a=b
- 31Trans (not equal)a a
- 32Order (+)a a+c < b+c
- 33Order (x)c>0 and a ac
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- Flashcards on Theorems, created by Claudia Gaytan on 26/02/2018.
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- Claudia Gaytan
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