Livin' the SLOG Life

Hello everybody! I am hoping all of you have had a nice Thanksgiving, and I hope you all aren't swamped by a huge wave of tests and assignments as I am! Today I would like to talk about floors. No, not the one you're standing on or the thing that's supporting your chair right now, I'm talking about mathematical floors! They are these magical things that sort of remove the decimals from any positive real numbers. The reason why I limit it to positive numbers in the previous statement is because they do something that looks different to negative numbers. Let's look at the definition of a floor that was given to us during class: At first glance, this looks preeeetty long and exhaustive, but really, all it's saying is that: 1. The floor of x is an integer 2. The floor of x is smaller than or equal to x and  3. For any integer that is smaller than x, it will be smaller than the floor of x (that is, the floor of x is the largest integer that is smal...

Hello readers!! Welcome to the end of Week 6 of classes and I hope that everyone has done well for the first term test. For me, this was quite the experience, as I've never felt so unsure about my own answers, but we shall see in probably a week or 2's time. I do apologize for not writing over the Thanksgiving break, but I assure you that I will be back on track for the rest of the semester! Today I'd like to talk about the different ways to prove things. I won't be going into all of them, as some are more self explanatory than others, but I will talk about the ones that I find rather confusing right now, just so I can use this post to help myself sort out some things. Proof by cases: When encountering a statement in which you feel that there is more sides to the statement to look at than what you can prove with just one line of thought, then we use proof by cases. We must, of course, think about all the different cases that are possible first, and then we prove...

Hello readers! Today I would like to talk to you about this week's newest topic: Proofs! (Because I'm sure you've all read enough about how easy or difficult the first assignment was). Since they have just been introduced to us, I am definitely no expert in the field, however I have to say that this is definitely an art, that is, a very accurate art. To create a proof for a statement takes true creativity and "out-of-the-box" thinking, while having to keep all the parts within it logically valid and true.  To me, making a proof is like making a burger: you have your standard buns (the outline of the proof) and then you're essentially free to put whatever you want between those buns, as long as it's edible and the flavours are coherent and harmonious. Further, just like how a BLT can't be missing any of those 3 ingredients that make it a BLT, you also can't just take out steps wherever you please. Creating cool new burgers is an art and ...