Statements Bernd Schr oder logo1 Bernd Schr oder Louisiana Tech - - PowerPoint PPT Presentation

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Statements

Bernd Schr¨

• der

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

A statement or proposition is a sentence that is either true or false.

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

A statement or proposition is a sentence that is either true or false.

• 1. Any mathematical result is a statement.

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

A statement or proposition is a sentence that is either true or false.

• 1. Any mathematical result is a statement.
• 2. Ideally, so is every sentence in a proof

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

A statement or proposition is a sentence that is either true or false.

• 1. Any mathematical result is a statement.
• 2. Ideally, so is every sentence in a proof, but prose can be

used to explain and loosen up the structure.

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

A statement or proposition is a sentence that is either true or false.

• 1. Any mathematical result is a statement.
• 2. Ideally, so is every sentence in a proof, but prose can be

used to explain and loosen up the structure.

• 3. We need not know whether a statement is true or false to

identify it as a statement.

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Following is a Statement?

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Following is a Statement?

• 1. The number 97 is prime.

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Following is a Statement?

• 1. The number 97 is prime. (Statement.)

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Following is a Statement?

• 1. The number 97 is prime. (Statement.)
• 2. The number 97 is a twin prime.

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Following is a Statement?

• 1. The number 97 is prime. (Statement.)
• 2. The number 97 is a twin prime. (Statement.)

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Following is a Statement?

• 1. The number 97 is prime. (Statement.)
• 2. The number 97 is a twin prime. (Statement.)
• 3. Which of the following is a statement?

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Following is a Statement?

• 1. The number 97 is prime. (Statement.)
• 2. The number 97 is a twin prime. (Statement.)
• 3. Which of the following is a statement? (Not a statement.)

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Following is a Statement?

• 1. The number 97 is prime. (Statement.)
• 2. The number 97 is a twin prime. (Statement.)
• 3. Which of the following is a statement? (Not a statement.)
• 4. All zeros of the Riemann Zeta function ζ(z) =

∞

∑

n=1

1 nz lie

• n the straight line ℜ(z) = 1

2.

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Following is a Statement?

• 1. The number 97 is prime. (Statement.)
• 2. The number 97 is a twin prime. (Statement.)
• 3. Which of the following is a statement? (Not a statement.)
• 4. All zeros of the Riemann Zeta function ζ(z) =

∞

∑

n=1

1 nz lie

• n the straight line ℜ(z) = 1
• 2. (Statement.)

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Following is a Statement?

• 1. The number 97 is prime. (Statement.)
• 2. The number 97 is a twin prime. (Statement.)
• 3. Which of the following is a statement? (Not a statement.)
• 4. All zeros of the Riemann Zeta function ζ(z) =

∞

∑

n=1

1 nz lie

• n the straight line ℜ(z) = 1
• 2. (Statement.)
• 5. c2 = a2 +b2 −2abcos(γ).

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Following is a Statement?

• 1. The number 97 is prime. (Statement.)
• 2. The number 97 is a twin prime. (Statement.)
• 3. Which of the following is a statement? (Not a statement.)
• 4. All zeros of the Riemann Zeta function ζ(z) =

∞

∑

n=1

1 nz lie

• n the straight line ℜ(z) = 1
• 2. (Statement.)
• 5. c2 = a2 +b2 −2abcos(γ). (Not a statement.)

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Statements We Gave are True?

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Statements We Gave are True?

• 1. The number 97 is prime.

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Statements We Gave are True?

• 1. The number 97 is prime. (True statement.)

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Statements We Gave are True?

• 1. The number 97 is prime. (True statement.)
• 2. The number 97 is a twin prime.

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Statements We Gave are True?

• 1. The number 97 is prime. (True statement.)
• 2. The number 97 is a twin prime. (False statement.)

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Statements We Gave are True?

• 1. The number 97 is prime. (True statement.)
• 2. The number 97 is a twin prime. (False statement.)
• 3. All zeros of the Riemann Zeta function ζ(z) =

∞

∑

n=1

1 nz lie

• n the straight line ℜ(z) = 1

2.

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements

logo1 Definition Examples Truth Values

Which of the Statements We Gave are True?

• 1. The number 97 is prime. (True statement.)
• 2. The number 97 is a twin prime. (False statement.)
• 3. All zeros of the Riemann Zeta function ζ(z) =

∞

∑

n=1

1 nz lie

• n the straight line ℜ(z) = 1
• 2. (We don’t know. This is

called the Riemann Hypothesis.)

Bernd Schr¨

• der

Louisiana Tech University, College of Engineering and Science Statements