Week #1

Week 1

#2
-Building sets in math

S = {1, 3, 5, 7, 9, 11}
5 in S? True
6 in S? False
{1,3} in S? True
{1,4} in S? False

{x| x in S and x>6}
{7, 9, 11}

{x+2| x in S and x>6}
{9, 11, 13}

-Building sets in Python

S = {1, 3, 5, 7, 9, 11}
# Python doesn't look like this

{x for x in S and x>6}
    |    ∈

# Use these
# In python, elements do not reappear
{x for x in S if x>6}
{x+2 for x in S if x>6}

>>> Danny = {x for x in S if x>6}
>>> Danny
{9,11,17}
>>> any({False, False, False})
False
>>> any({True, False, False})
True
>>> all({False, True, True})
False
>>> all({True, True, True})
True
>> all({})
True

#3
def qo(S1, S2):
    return not all({x in S2 for x in S1})
    # Some element of S1 is not an element of S2.


def q1(S1, S2):
    return any({x in S2 for x in S1})
    # Some element of S1 is an element of S2

def q1(S1, S2):
    return all({x in S2 for x in S1})
    # Every element of S1 is an element of S2
    # We include the situation that the set is an empty set

def q3(S1, S2):
    return not any({x in S2 for x in S1})
# Every element of S1 is not an element of S2
# This also works when S1 is an empty set

Rigor without morits
1) Understand the problem
 * Know what's given
 * What's required
 * Re-state the problem in your own words/ draw some diagrams

2) Plan solution(s)
 * Try come up different approaches

3) Carry out your plan:
 * WRITE IT DOWN

4) Review



Thoughts:

This week is the first week of university and our prof talked about sets.
And during the lecture, I found two things that are tricky, the 'for' and the duplicates.

-'for'
For example, in the lecture notes the python command Danny = {x for x in S if x > 6} is hard to understand and hard to precisely describe it in English. However, our professor suggested that we can understand it in the term of | of sets in maths. For example Danny = {x | x in S and x > 6}. In sets of maths, things before 'for' are the expression of element in the actual sets and things afterwards are the conditions that the item have to satisfy. So that {x | x in S and x > 6} means that for all the possible values of x in the universe, if that value is in S and it is greater than 6, then we append that value of x to the set. Thus we got {7, 9, 11} as the final result. And {x+2 | x in S and x > 6} means that for all the possible values of x in the universe, if that value is in S and it is greater than 6, then we append x+2 to the set. Thus we got {9, 11, 13}. We can apply similar idea to help us understanding 'for' in creating sets in Python. For instance, {x for x in S if x > 6} means that for all the xes in S, if that x is greater than 6, then append it to the set.

- duplicates
We know that sets have some wonderful features. One of them is it automatically merge all the duplicates. By my friend's Shrey's idea, we can write a python program with only one line to merge all the duplicates in a list or check if there is duplicates in the list. Here are the code.

def merge_duplicates(lst):
    """(list) -> list
    return a list with all duplicates merged.
    """
    return list(set(lst))

def contain_duplicates(lst):
    """(list) -> boolean
    return True if there is no duplicate in the list given.
    """
    return len(lst) == len(set(lst))

And this is very helpful in our CSC148 assignment.