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Week 7: Get to know your floor

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 smaller or equal to x)

 Pretty simple right? So now you might be able to understand why I didn't say that this function just removed the decimals of numbers, since the floor of a negative number, say, -3.14, would be -4, instead of being -3 like what would happen if we just took away that decimal.

 I will just leave it there today for you to contemplate, have a nice week my lovely readers! 
Lana :)
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