What are we doing with our lives?
So as I was looking through my notes to figure out what I should write about in my blog I kept coming across side notes saying look up Mantis Shrimp, therefore I did and hyperlinked the website to show us that we are going insane. But I must say this shrimp is pretty awesome and The Oatmeal does a great depiction on the mantis shrimp.
On another note, I think it would be interesting if we talked about why |(0,1) X (0,1)|=|(0,1)|. The first thing I do any problem like this is draw the two figures: a line segment from 0 to 1 and a cube with the dimensions from the origin (0,1). If we first look at the line segment we know that the segment 0 to 1 is part of the R which means that there are an infinite amount of numbers between (0,1). But if we take a segment from the line segment, 0 to .0001 we also know that interval is also R which also means there is an infinite amount of numbers. One way we determine that these figures all contain the same points is to prove that each of the figures are bijective (onto and one-to-one). The first question is we know that it is onto due to the shadow function, but how do we know it is one to one? The shadow function it alternating between digits after the decimal between x and y functions. For instance x=.12345678 and y=.2314678 the shadow function would look something like: 0.1231……etc.
Convex sets. scavenger
I really just think that this definition is pretty neat and I feel better knowing that this was a question on the previous exam, since everyone in our class pretty much understood the concept. Just to summarize since this a homework question, a convex set is when two points (x,y) and (a,b) lie in the sam e plane and can be connected by a line segment. One way to prove that a convex exist in a plane is to prove that the two points are equal to each other. Another way to prove a convex set is to let E=R^2. A nonconvex set is on a plane that has a cut out, in which two points can have a line segment that is not contained on the plain.
DON’T FORGET ABOUT OUR SCAVENGER HUNT THIS WEEK!!
s through FOM we only have 3 classes left…bitterssweet.