# Cecilia’s Reflection Week 12

December 6, 2011
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It has been a long week. I don’t even know if “it” is used correctly in the previous sentence since it has no preceding noun that explains what it is. However, I think the general reader can figure out that “it” means “this week,” which would seem really repetitive and awkward (another grammar error) if I actually wrote the sentence that way.

The grammar of ambiguous pronouns aside, this week we learned more about functions and relations and sets. We revisited function compositions with the discrete math function $f:\mathbb{Z}^{\geq 0} \rightarrow \mathbb{Z}$, defined by the rule $f(x)=3x-5$, instead of the algebra function $y=3x-5$. Other than this format change, function compositions, or the function of a function ($f\circ g$), were things to review. I was about to write “was review,” but then I realized that that would break the subject-verb number agreement.

Arrow diagrams of function compositions give me lots of delight (I tried to think of a better, more suitable word but failed) because they involve seeing two arrow diagrams as one by combining the middle one. Other than some limitations with the domain and codomains, this was just like my story diagrams that I have made ever since first grade. Here, I’ll make one. This is for my Young Authors story called “Apples.” It just won in my school, but in county? I’m waiting anxiously for results.

My Young Authors story function composition arrow diagram, edited down to 3 pages from 5 pages

As you can see, it’s pretty cliché and unoriginal. Hopefully my fancy language can make up for that, though. It does work wonderfully in an arrow diagram. “Page 1″ is actually a function!

We also learned about invertible functions, which happens only when a function is one-to-one and onto with another function. The two functions must be inverses.

One-to-one means that each input value only has one output value. Onto means that the codomain is equal to the range. The relations in my diagram are both onto, but only the first one is one-to-one.

Yes, Colin. I am excited to get into All State again, especially because I messed up my audition and I’m now a two year vet! (and so did you)

I was a bit confused about cardinality though. It took me about two and a half hours staring at that one sentence in our notes for my brain to process what it meant. I think it’s slow because I’m so used to rereading and editing my story. Even then, I had to go back and read the definition of cardinality every five minutes as I did my CTQs.

We also learned that infinite sets could be countable because the mathematical definition is different from the standard definition. This irks me because I am so used to the confines of fiction stories and deep poems, not math notes. “An infinite set is uncountable if it is not countable.” Oh my cloud. That made me laugh because I normally disapprove of repetitive, obvious statements because they are grammatically awkward, but this sentence was actually grammatically correct.

I would have recorded a song this week, but my voice is still gone, unfortunately. It’s improving, but I don’t want to risk talking in case I ruin it all over again. My voice is surprisingly fragile for somebody who sings.

First reflection! Yay!

lovelovelove,

Cecilia, who just realized that she did her CTQs all wrong so she will go and rethink all the problems now. She believes that writing this reflection has made her fingers stronger for piano and gained a more profound understanding of this week’s math. She is hitting two birds with one stone. She loves talking in third person. She does not think that it is awkward at all.

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## Quotations

“What we want is to see the child in pursuit of knowledge, and not knowledge in pursuit of the child.” ~ George Bernard Shaw