I started by pulling up Webster's online dictionary and searching the word, "transcendental." I was directed to the definition of "transcendent". This is defined as "going beyond the limits of ordinary experience," or "far better or greater than what is usual." Now, I don't think that reveals to me how the word is related to math, but I do think that I can think of it in such a way that it does. For example, maybe we are studying transcendental functions because we want to take our minds to a place where they go beyond the limits of an ordinary mathematical experience, or because we want to study mathematics in a way that is far better or greater than what is usual. These definitions and applications intrigued me.
Next, I found out what transcendentalism is. It is a practice that I am not sure I am in agreement with, but that is interesting to ponder. It is a practice of people who do not accept things as religious beliefs, but rather as a way of understanding life's relationships. This also got my "math brain" thinking. Maybe we are studying transcendental functions because we want to study the relationships between numbers and equations. We want to discover how things work together in a mathematical context.
Finally, as I did research on transcendental functions themselves, I found my wonderings to be almost correct. Transcendental functions have the name they do because they cannot be expressed simply. They cannot be expressed using simple algebra. They allow us, and force us, to go deeper into our mathematical thinking.
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