Algebra 2 - Miss Stanley`s Algebra Wiki
... - Based on this, call on a student to put the irrational number circle on the board. With discussion, the class should understand that this circle must be mutually exclusive. - Explain that these numbers together are considered real numbers; draw in a final circle to complete the diagram. - Write al ...
... - Based on this, call on a student to put the irrational number circle on the board. With discussion, the class should understand that this circle must be mutually exclusive. - Explain that these numbers together are considered real numbers; draw in a final circle to complete the diagram. - Write al ...
Numbers, proof and `all that jazz`.
... Since the time of Euclid, lists of axioms for many fields of mathematics, such as set theory, logic, and numbers have been compiled. In these notes, we present one of the standard lists of axioms for the real numbers, which are the numbers used in calculus. Thus, we are stating “up front,” those pro ...
... Since the time of Euclid, lists of axioms for many fields of mathematics, such as set theory, logic, and numbers have been compiled. In these notes, we present one of the standard lists of axioms for the real numbers, which are the numbers used in calculus. Thus, we are stating “up front,” those pro ...
Infinitesimal Complex Calculus
... ε alludes to the hyper-real infinitesimals. But infinitesimals do not exist on the real line, or in the complex plane, and cannot be used in the Calculus of Limits. Thus, to derive the Cauchy Integral Formula, we need the Complex Infinitesimals. ...
... ε alludes to the hyper-real infinitesimals. But infinitesimals do not exist on the real line, or in the complex plane, and cannot be used in the Calculus of Limits. Thus, to derive the Cauchy Integral Formula, we need the Complex Infinitesimals. ...
Math 90 Lecture Notes Chapter 1
... had dropped to –10 degrees. (10 degrees below zero). What was the difference between the temperature at 10:00am and 3:00pm? a. This problem also used subtraction, but in a more general sense. Notice the word difference implies subtraction. This problem would translate into the following: 20 – (-10) ...
... had dropped to –10 degrees. (10 degrees below zero). What was the difference between the temperature at 10:00am and 3:00pm? a. This problem also used subtraction, but in a more general sense. Notice the word difference implies subtraction. This problem would translate into the following: 20 – (-10) ...
A sequence - Hatboro
... A sequence is an ordered list of numbers. The sum of the terms of a sequence is called a series. While some sequences are simply random values, other sequences have a definite pattern that is used to arrive at the sequence's terms. Two such sequences are the arithmetic and geometric sequences. Let's ...
... A sequence is an ordered list of numbers. The sum of the terms of a sequence is called a series. While some sequences are simply random values, other sequences have a definite pattern that is used to arrive at the sequence's terms. Two such sequences are the arithmetic and geometric sequences. Let's ...
A Radical Approach to Computation with Real Numbers
... Run-length encoding of a contiguous block of 1s amongst 256 bits only takes 16 bits. 00000000 00000000 means all 256 bits are 0s xxxxxxxx 00000000 means all 256 bits are 1s (if any x is nonzero) 00000010 00000110 means there is a block of 2 1s starting at position 6 ...
... Run-length encoding of a contiguous block of 1s amongst 256 bits only takes 16 bits. 00000000 00000000 means all 256 bits are 0s xxxxxxxx 00000000 means all 256 bits are 1s (if any x is nonzero) 00000010 00000110 means there is a block of 2 1s starting at position 6 ...
Cauchy Sequences
... In any metric space S, a divergent Cauchy sequence, because it “converges to a hole,” detects a hole into which S could fit another point. A metric space that has no such holes is called a complete metric space: Definition 4 A metric space S is complete iff every Cauchy sequence in S has a limit in ...
... In any metric space S, a divergent Cauchy sequence, because it “converges to a hole,” detects a hole into which S could fit another point. A metric space that has no such holes is called a complete metric space: Definition 4 A metric space S is complete iff every Cauchy sequence in S has a limit in ...