I think I got the definition wrong. It should be (i think)
##(X,\tau)## is ##T_0## if for any distinct points ##x,y \in X##, we can find an open set ##U## such that ##x \in U## and ##y \notin U## or ##x \notin U## and ##y \in U##.
So in post #2, we can't guarantee there is an open set...
Sorry for the really dumb question, but is there an example where we can't replace the statement with: ##(X, \tau)## is ##T_0## if and only if for all ##x \in X##, ##\lbrace x \rbrace'## is empty? (I know ##\emptyset## is closed but...)
Definition: ##(X,\tau)## is ##T_0## if for any distinct...
The above should be ##(N \cdot N)(n) = \ldots = (N\sigma_0)(n)##. (why?)
I think this is a right idea but there is a lot being used without explicit mention, which i think maybe makes it hard to follow. Somewhere we might mention "We will write the Dirichlet product of two arithmetic functions...
I have a little trouble following it, but it looks like you've made a mistake in distribution e.g., ##(A \cup B) \cup Z \neq (A \cup Z) \cap (B \cup Z)## in general.
We have ##P(Y \cup Z) = P(Y) + P(Z) - P(Y \cap Z)##. We can then apply I/E to ##P(Y)## (i'll leave that to you). We can also use...
I had not thought of that. Rereading this thread, I completely agree with the points made by Mark and Perok and hope the OP understands them. I think i was mainly just reacting to some of the things in post #4.
Apologies and hopefully the thread gets back on track.
What's wrong with it? In the OP, they use the theorem that to show ##n## is prime, it is sufficient to show all primes ##p \le \sqrt{n}## do not divide ##n##.
In fact, I really don't see anything wrong with the OP. Maybe other than writing something like ##\lfloor \sqrt{1949} \rfloor = 44##.
ok so far. I'd rewrite the last two sentences as "Choose ##p = n! - 1##. Then ##n < p < n!## since ##n > 2##.
Since the argument below shows such a prime ##n < p## exists, you shouldn't assume its existence here. The above sentence should be "Let ##p## be a prime factor of ##n! - 1##". We don't...
It's not clear to me why such a prime ##p## exists. (referring to "
Let ## p ## be a prime factor of ## n!-1 ## such that ## n<p ## for some ## n\in\mathbb{N} ##
where ## n>2 ##." which won't quote for some reason).
Here is where you've shown such a prime ##p## exists.
Looks good to me. But...
Sorry... I just read the course page and it says I should be using python 3.5. Running the above code in Python 3.5. gets rid of the error. (and gives a new one! but hopefully i can fix that.)
# Test suite for Problem Set 3 (Simulating Robots)
# Fall 2016
import sys
import threading
import traceback
import unittest
import random
import imp
test = imp.load_compiled("test", "test.pyc")
import ps3
def xyrange(x_upper_bound, y_upper_bound):
""" Returns the cartesian product of...
Now it works, I forgot to return g in the buildCityGraph.
class Node(object):
def __init__(self, name):
self.name = str(name)
def get_name(self):
return self.name
def __str__(self):
return self.name
class Edge(object):
def __init__(self, src, dest)...