SUNY Geneseo Department of Mathematics

Statements Discussion

Math 239 03
Spring 2021
Prof. Doug Baldwin

(The following is/are the initial prompt(s) for an online discussion; students may have posted responses, and prompts for further discussion may have been added, but these things are not shown.)

This online discussion, and its continuation in class on Friday (Feb. 5), are your chance to practice thinking about and working with the concept of a mathematical statement or “proposition.” Please think about the following, and post counter-questions, comments, answers, etc. as you wish.

Definition

Which of the following meet the definition of a mathematical statement? Why or why not? For some of these, answers may depend on exactly how you interpret the English phrase — take that as opportunity to discuss different interpretations and how they lead to different answers.

  1. It sometimes snows in Geneseo.
  2. It snowed in Geneseo on February 1, 2021.
  3. SUNY Geneseo is the best college.
  4. It rained in Geneseo on June 7, 1849.
  5. Go Knights!
  6. There is some integer x such that 3x + 2 = 11.
  7. To solve the equation 3x + 2 = 11, subtract 2 from both sides and then divide by 3.
  8. Is x = 3 a solution to 3x + 2 = 11?
  9. x = 3 is a solution to 3x + 2 = 11.
  10. x = 4 is a solution to 3x + 2 = 11.
  11. x = 3 is a solution to 3x + 2 = 11 and so is x = 4.
  12. Read a book.
  13. This statement is false.

Is it possible for an English statement to be true without being a mathematical statement?

Truth and Falsehood

See if you can make progress towards deciding whether the following statements are true or false, and comment on how you do, or could do, it. I don’t expect that you will reach definite conclusions on each; thinking about processes is more important than definite answers here.

  1. There is some integer x such that 3x + 2 = 11.
  2. For all integers x, 3x + 2 = 11.
  3. For every integer n > 2, there are no integers a, b, and c such that an + bn = cn.
  4. For every integer n > 4, every nth-degree polynomial has at least one non-integer root.
  5. Every even integer greater than 2 is the sum of two prime numbers.
  6. At noon on February 6, 2021, atmospheric pressure in Geneseo will have been between 14.68 and 14.72 pounds per square inch.