1. The most important thing we have to discuss is that my tickets for Calculus the Musical have been reserved. BOSS.
2. In regards to the reading, I am excited that I understand what the horizontal and vertical line tests we all did in elementary algebra actually were telling us. The vertical line test is how we can tell (from the graph) that a graph is a function. We can know for certain that what we're seeing is a function, because every value of the set A is assigned exactly one value of the set B. The horizontal line test is how we can tell (from the graph) that a function is one-to-one. We can know for certain that it is one-to-one because every value of the set A is assigned exactly one unique value of the set B. Fascinating.
3. My weak understanding of these function things basically just tells me that bijective sets are the sets formed when the cardinality of A and the cardinality of B are the same, such that every value of A has a unique value B. This makes the function of A and B linear, onto and one-to-one. I can see that this would be useful, as there are many things in mathematics that depend on weather or not something in linear...and now we can know by simple Math 290 mapping! (Or we could just do the horizontal/vertical line test. Whatever works.
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