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CS103A
HO #6
SlidesIntro to Proofs
1/14/08
1
What is a proof?
Science
: "prove" a hypothesis using inductive reasoning,
i.e., the scientific method.
We gather bits of specific information together and use
our own knowledge and experience in order to make an
observation about what must be true.
Does not produce mathematical certainty.
Everyday example:
Observation: John came to class late this morning.
Observation: John’s hair was uncombed.
Prior experience: John is very fussy about his hair.
Conclusion: John overslept
1 =
1
1 + 3 =
2
1 + 3 + 5 =
3
1 + 3 + 5 + 7 =
4
Do we ever use inductive reasoning in mathematics?
Yes, we use it to form hypotheses.
2
2
2
2
What is a proof?
Law
: convince one set of 12 people, or a judge, none
of whom may be experts in the subject matter, that
your explanation is valid.
Can use deductive and inductive
reasoning, precedent, psychological tricks, etc.
What is a proof?
Math
: we do proofs with deductive reasoning and the
rules of logic.
A proof is a stepbystep demonstration that a conclusion
follows from some premises.
Each step is a logical consequence of the ones that come
before it.
All proofs must be
rigorous
.
That is, each step in a proof
must provide definitive evidence that the intermediate
conclusion follows from things already established.
(a) If my glasses are on the kitchen table, then I saw them at breakfast.
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 Winter '07
 Plummer,R
 Computer Science

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