notes10_6.pdf
... sequence. A sequence can also be represented in the abbreviated form {a n }, where the symbol for the nth term is placed between braces. We refer to the sequence as the sequence {2n – 1}. The sequence can either be a finite sequence, where we know how many terms we want to list, or it can be an infi ...
... sequence. A sequence can also be represented in the abbreviated form {a n }, where the symbol for the nth term is placed between braces. We refer to the sequence as the sequence {2n – 1}. The sequence can either be a finite sequence, where we know how many terms we want to list, or it can be an infi ...
SAT Numbers
... numbers are mutually exclusive. Any given number must be either rational or irrational; no number can be both. Real Numbers. Every number on the number line. The set of real numbers includes all rational and irrational numbers. Imaginary Numbers. See the “Miscellaneous Math” chapter later in this bo ...
... numbers are mutually exclusive. Any given number must be either rational or irrational; no number can be both. Real Numbers. Every number on the number line. The set of real numbers includes all rational and irrational numbers. Imaginary Numbers. See the “Miscellaneous Math” chapter later in this bo ...
Week 1
... • If a negative numbers is multiplied or divided by a negative number, then the answer is positive. • If a negative numbers is multiplied or divided by a positive number, then the answer is negative. • If a positive numbers is multiplied or divided by a negative number, then the answer is negative. ...
... • If a negative numbers is multiplied or divided by a negative number, then the answer is positive. • If a negative numbers is multiplied or divided by a positive number, then the answer is negative. • If a positive numbers is multiplied or divided by a negative number, then the answer is negative. ...
PDF
... instance of the schema B ↔ C by assumption, the result follows directly if we assume B ↔ C is a theorem schema. Using the substitution theorem, we can easily derive more theorem schemas, such as 7. (A → B) ↔ (¬B → ¬A) (Law of Contraposition) 8. A → (¬B → ¬(A → B)) 9. ((A → B) → A) → A (Peirce’s Law ...
... instance of the schema B ↔ C by assumption, the result follows directly if we assume B ↔ C is a theorem schema. Using the substitution theorem, we can easily derive more theorem schemas, such as 7. (A → B) ↔ (¬B → ¬A) (Law of Contraposition) 8. A → (¬B → ¬(A → B)) 9. ((A → B) → A) → A (Peirce’s Law ...
9.6 Add and Subtract Negative Mixed Numbers
... 7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom h ...
... 7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom h ...
Mathematical Reasoning (Part III)
... COROLLARY 17. The equation m2 − 4n = 2 has no integer solutions. COROLLARY 18. If the square of an integer is divided by 4, the remainder cannot be equal 2. COROLLARY 19. The square of an integer cannot be of the form 4n + 2, n ∈ Z. PROPOSITION 20. Let a, b, and c be integers. If a2 + b2 = c2 then a ...
... COROLLARY 17. The equation m2 − 4n = 2 has no integer solutions. COROLLARY 18. If the square of an integer is divided by 4, the remainder cannot be equal 2. COROLLARY 19. The square of an integer cannot be of the form 4n + 2, n ∈ Z. PROPOSITION 20. Let a, b, and c be integers. If a2 + b2 = c2 then a ...
2340-001/lectures - NYU
... • For all integers m and n, if m+n is even then m and n are both even or m and n are both odd • The product of any non-zero rational number and any irrational number is irrational • If a, b, and c are integers and a2+b2=c2, must at least one of a and b be even • Can you find two irrational numbers s ...
... • For all integers m and n, if m+n is even then m and n are both even or m and n are both odd • The product of any non-zero rational number and any irrational number is irrational • If a, b, and c are integers and a2+b2=c2, must at least one of a and b be even • Can you find two irrational numbers s ...
