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Mathematical Analysis
Mathematical analysis is, simply put, the study of limits and how they can be manipulated. Starting with an exhaustive study of sets, mathematical analysis then continues on to the rigorous development of calculus, differential equations, model theory, and topology. Topics including real and complex analysis, differential equations and vector calculus can be discussed in this category.
2,575 Questions
Iteration is a process where you use your previously obtained answers in your next equation. Consider the equation x_(n+1)=x_(n)+4. Where n is an arbitrary non negative integer.
We must be given an original x_0 say x_0=1 here. Then
x_1=x_0+4=5
x_2=x_1+4=9
x_3=x_2+4=13
and so on....
What is a 'unit'? A unit could be one pint, then the answer is 1000. Or one un it could be a quart, then the answer is 500.
What is the difference between the primal and dual?
The difference between primal and dual are that primal means an essential, or fundamental of an aspect where as dual means consisting of two parts or elements. Primal is one, dual is two.
71 : Python code that demonstrates this.
N = 1 while True : if N % 8 8 : print N break N += 1
It is a length measure that equals 200 centimeters
1 foot = 0.3048 meters = 12 inches
so, 2 meters = 2/0.3048 feet = 6.56 feet or = 6 feet 6.72 inch
How do you write one hundred eighty six thousand in numbers?
It is 186.000 miles per hour using measurement units which are used mainly in the US. In miles per second, this is the speed of light in vacuum. Although the English (technically the British) do use miles to measure distance, the speed of light is a scientific measure and the British would use kilometres per second as the appropriate measurement units.
How do you define a metric space through the use of sets?
The concept of a distance, or metric, between the elements of a set is well defined in topology. Let B be any set with x, y, z Є B, and let D be a function from the Cartesian product, B X B, into the set of real numbers, R. D is called a metric on B if the following four statements hold:
1) D(x,y) ≥ 0 for all x, y
2) D(x,y) = D(y,x) for all x, y
3) D(x,y) = 0 if and only if x = yfor all x, y
4) D(x,y) + D(y,z) ≥ D(x,z) for all x, y, z
In this case, the set B having metric D is called a metric space, and is often notated as B, D.
For more information and related definitions, see the links below.
2d means 2 dimensional or flat figures. If you are dealing with algebra or graphing, it would mean X and Y coordinates only, not Z.
What might be the advantages of using the archival method?
to storge the method in until a later day .tat way it give the man time to think about what is being said before answering the question.
What is the relation between ordinary differentiation and partial differentiation?
in case of partial differentiation ,
suppose a z is a function of x and y
so in partial differentiation of z w.r.t x all other variables except x are considered to be constant
but on the contrary in differentiation process they are not considered as constant unless stated .
Conduct your sampling at a baseball game, a baseball museum or at a meeting of Little League coaches.
Why do most Americans put a much higher value on looks than on intellect?
That is a generalization that is not neccessarily true. This is an assumption that everyone feels, acts, or thinks the same. Not everyone puts a higher value on looks. In today's society, people who place a higher value on looks are the ones that were never taught any better. I personally would much rather spend time with someone who uses their brain than with someone who is easy to look at.
Assuming that you want to discount luck (if not, the answer would be 1), and that the guesser always guesses the median of the remaining range, the answer would be the (ceiling of the log(base 2) of the count of numbers in the range). If the log(base 2) is an exact integer, add 1.
Example 1, pick a number between 1 and 9. There are 9 numbers in the range, so the log(base2) of 9 is ~3.16. The ceiling of that is 4. Do not add 1 for a final answer of 4.
The full range is 1,2,3,4,5,6,7,8,9. The median is 5
First guess is 5. Higher - 6,7,8,9 is remaining range. 7 and 8 are the median numbers
Second Guess is 8. Lower - 6,7 is the remaining range. 6 and 7 are the median numbers.
Third guess is 7. Lower - 6 is the remaining range. 6 is the median number
Fourth guess is 6. Correct.
Example 2, pick a number between 1 and 16. There are 16 numbers in the range, so the log(base 2) of 16 is 4. The ceiling of 4 is 4. Add the 1 because the Log(base 2) is an integer, for a final answer of 5.
Full range is 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16. The median numbers are 8 and 9.
First Guess is 9. Lower - 1,2,3,4,5,6,7,8 is the remaining range. 4 and 5 are the median numbers
Second Guess is 4. Higher - 5,6,7,8 is the remaining range. 6 and 7 are the median numbers.
Third Guess is 6. Higher - 7,8 is the remaining range. 7 and 8 are the median numbers.
Fourth Guess is 7. Higher - 8 is the remaining range. 8 is the median.
Fifth guess is 8. Correct
Both of these examples show worst case scenarios. A "lucky guess" will reduce the number of guess needed, possibly all the way to 1.
Note: I do realize that to a math purist, in the examples where I said that the median numbers were x and y, the correct answer is that the median number is between x and y. Since I can not guess the number between the two numbers, I am bending the definition of median to treat the two bordering numbers as the median when the strict definition would list the median as being between those two numbers.
Who does the set theory explain about sets?
Who: Basically, the set theory was developed by Georg Cantor.
