Week 6
This week we were introduced to a new class of functions, the non-boolean functions.
These are special functions like, for example $sin(x)$, which take an input and give an integer a
real output. This differs from all other functions, which are predicates, returning only True or False.
I felt really excited about how we could incorporate these functions with
our "tool-box of instruments", to put metaphorically, implications, quantifiers, conjunctions
and disjunctions, to prove a greater range of statements.
The first, arguably special non-boolean function we were introduced to was "floor".
The "floor" function ($\lfloor x \rfloor$)is defined as:
$\lfloor x\rfloor\in\mathbb{Z}\wedge\lfloor x\rfloor\leq x\wedge(\forall z\in\mathbb{Z}, z \leq x \Rightarrow z \leq \lfloor x \rfloor)$
It's simply just taking the largest integer for any real number.
I found that I grasped the concept of floor quickly, as I did a high school research project on the function and it's intrinsic properties. I could say that I enjoyed learning about this function!
I also believe that disproofs also deserve a mention this week, as we have not learn't much about the
formal way of disproving statements. Turns out it is just proving the negation.
Now, I should start work on assignment 2...
This week we were introduced to a new class of functions, the non-boolean functions.
These are special functions like, for example $sin(x)$, which take an input and give an integer a
real output. This differs from all other functions, which are predicates, returning only True or False.
I felt really excited about how we could incorporate these functions with
our "tool-box of instruments", to put metaphorically, implications, quantifiers, conjunctions
and disjunctions, to prove a greater range of statements.
The first, arguably special non-boolean function we were introduced to was "floor".
 |
| NO! Not that one! |
$\lfloor x\rfloor\in\mathbb{Z}\wedge\lfloor x\rfloor\leq x\wedge(\forall z\in\mathbb{Z}, z \leq x \Rightarrow z \leq \lfloor x \rfloor)$
It's simply just taking the largest integer for any real number.
I found that I grasped the concept of floor quickly, as I did a high school research project on the function and it's intrinsic properties. I could say that I enjoyed learning about this function!
I also believe that disproofs also deserve a mention this week, as we have not learn't much about the
formal way of disproving statements. Turns out it is just proving the negation.
Now, I should start work on assignment 2...
