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Integers on a Number Line
... Remember negative numbers are to the left of zero, and positive numbers are to the right of zero. As you move to the left on a number line the value of the numbers decrease. As you move to the right on a number line the value of the numbers increase. ...
... Remember negative numbers are to the left of zero, and positive numbers are to the right of zero. As you move to the left on a number line the value of the numbers decrease. As you move to the right on a number line the value of the numbers increase. ...
Define
... Circumference - Distance around a circle Collinear points - Points that lie on the same line ...
... Circumference - Distance around a circle Collinear points - Points that lie on the same line ...
real number line
... If wind resistance is ignored, an object falling close to Earth’s surface falls at a rate of 32 ft/sec. What are the object’s velocity and ...
... If wind resistance is ignored, an object falling close to Earth’s surface falls at a rate of 32 ft/sec. What are the object’s velocity and ...
Power Point over Rational and Irrational Numbers
... as a ratio of two integers. • A rational number written in decimal form is terminating or repeating. ...
... as a ratio of two integers. • A rational number written in decimal form is terminating or repeating. ...
Continued Fraction Notes (Merry Christmas!)
... (b) The numbers An and Bn satisfy the Fibonacci-like rule: An = an An−1 + An−2 and Bn = an Bn−1 + Bn−2 for n ≥ 2 Proof. (a) is from the definition, and (b) follows from Corollary 2. Example. Taking the sequence 3, 7, 15, 1 again, we have: A0 = 3, A1 = 22, A2 = 15 · 22 + 3 = 333, A3 = 1 · 333 + 22 = ...
... (b) The numbers An and Bn satisfy the Fibonacci-like rule: An = an An−1 + An−2 and Bn = an Bn−1 + Bn−2 for n ≥ 2 Proof. (a) is from the definition, and (b) follows from Corollary 2. Example. Taking the sequence 3, 7, 15, 1 again, we have: A0 = 3, A1 = 22, A2 = 15 · 22 + 3 = 333, A3 = 1 · 333 + 22 = ...
The NumbersWithNames Program
... Prunes uninteresting conjectures Sorts conjectures by plausibility ...
... Prunes uninteresting conjectures Sorts conjectures by plausibility ...
Rational Numbers
... second number, the sum is equal to the second number (example : 4 + 0 = 4) Multiplicative Identity – A number such that when you multiply it by a second number, the product is equal to the second number (example: 4 x 1 = 4) Additive Inverse – Two numbers are additive inverses if their sum is the ...
... second number, the sum is equal to the second number (example : 4 + 0 = 4) Multiplicative Identity – A number such that when you multiply it by a second number, the product is equal to the second number (example: 4 x 1 = 4) Additive Inverse – Two numbers are additive inverses if their sum is the ...
Square roots
... There are many ways to see this fact, already accessible to us after the first lecture! (In case you are wondering why this might be interesting, it is rumoured that Hippassus of Metapontum was killed over his discovery of this fact, so this was a very astonishing and abrasive discovery at one time. ...
... There are many ways to see this fact, already accessible to us after the first lecture! (In case you are wondering why this might be interesting, it is rumoured that Hippassus of Metapontum was killed over his discovery of this fact, so this was a very astonishing and abrasive discovery at one time. ...
natural numbers
... But there is no rational number equal to PI. In fact, the reals are set up precisely to make completeness work. One way to construct the reals is to construct all convergent sequences of rationals and add new points to represent the limits of these sequences. (Most of the machinery of calculus depen ...
... But there is no rational number equal to PI. In fact, the reals are set up precisely to make completeness work. One way to construct the reals is to construct all convergent sequences of rationals and add new points to represent the limits of these sequences. (Most of the machinery of calculus depen ...