# Symbols for Sets * Symbolic math can be weird and intimidating. * The symbols in math are really *words in disguise*. --- # Analogy You don't want to write "I'm laughing so hard right now that tears are coming out of my eyes and my head is shaking from side to side." Instead you write :laughing: :rolling_on_the_floor_laughing: --- # Analogy, continued Mathematicians got tired of writing "Two times two times two times two" so they created $2 \cdot 2 \cdot 2 \cdot 2$ or $2^4$ to represent the same idea. --- # Understandability Each symbol that we use should be *clearly defined*. I have no doubt that you are intelligent enough to understand it. If it doesn't make sense, that's on me as the Instructor. E-mail me and let me know. --- # Set Membership ## A **set** has members. #### For instance, if we say * "Let A = {2,3,5,7}" then 2,3,5, and 7 are the **members** of the **set** A. --- # Set Inclusion We use the $\in$ symbol (pronounced "in") to show that something is an element of the set. For instance, if we say "Let A = {2,3,5,7}", then the statement "$2 \in A$" would be **true** and the statement $4 \in A$ would be **false**. --- # Set Inclusion Practice Let $B$ be the set { 1, 3, 5, 9 }. Which of the following is **true**? * $1 \in B$ * $2 \in B$ * $3 \in B$ * $11 \in B$ --- # Set Inclusion Practice Let $B$ be the set {1, 3, 5, 9 }. Which of the following is **true**? * $1 \in B$ :heavy_check_mark: **true** * $2 \in B$ :negative_squared_cross_mark: **false** * $3 \in B$ :heavy_check_mark: **true** * $11 \in B$ :negative_squared_cross_mark: **false** --- # Finite or Infinite? An interesting question about a set is whether it is *finite* or *infinite*. -- If you can't place a definite limit on the size of the set, the set is *infinite* $\infty$. -- If you can place such a limit, the set is *finite*. --- # Example Let $S$ be the set of students who are taking Math 193 in Spring 2021. **Question:** Is $S$ a *finite* or *infinite* set? --- --- # Example ## Let $S$ be the set of students who are taking Math 193 in Spring 2021. **Question:** Is $S$ a *finite* or *infinite* set? **Answer:** $S$ is a *finite* set. We know that there are fewer than 30 students in the class. --- # Question ## What are some examples of infinite sets? * This can be tricky. Many people think that the universe is infinite, but [that is unknown](https://astronomy.com/news/2020/03/is-the-universe-in##finite#:~:text=First%2C%20it's%20still%20possible%20the%20universe%20is%20finite.&text=The%20observable%20universe%20is%20still,13.8%20billion%20years%20to%20travel.) --- # Infinite Sets * An infinite set is one where, no matter how many items you have listed, there are. Listing all of the elements would take forever. * I want you to think of examples, but **please don't use "space" or "the universe": this actually is unknown.** --- # OK to search? It's defnitely OK to search the Internet for examples. Just remember that if you use a source, you need to acknowledge where you got the information. --- # You Try It Go back to Canvas and complete **Set Checkpoint 2.**