This week, we learnt proofs. Proofs require lots of
thinking. We learnt how to prove a non-boolean statement, how to disprove a
statement, and proof about limits. A non-boolean statement is usually likes a
function. Not a equation that returns true or false. A typical non-boolean
function is the ‘ the floor of x’. We cannot apply quantifiers to this
non-boolean function. And to disprove a
statement, we just need to prove the negate form of that statement. To prove a
limits, the order of quantifiers matter a lot. I can always think that given
such statement, how I can choose a statement to win the statement.
The proofs are challenging, especially the proofs about
limits. The proofs have specific formats, so I think the first thing I need to
do is to get familiar with the formats. The most important thought about proofs
is that I have to understand the statement clearly and need to believe the
statement is true. By following the format, then I need to practice a lot to
improve the thinking. There are many ways to prove a statement, so practice
will help a lot. And I believe there are some patterns for proofs. Like proving
an implication, while choosing the arbitrary numbers or functions, we can also
do the latter part first then come back to this function. Because it’s easier
and more accurate that way.
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