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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
Write thus:
3/1 x 3/10
Then multiply across:
3 x 3 = 9
1 x 10 = 10
Which gives the answer of 9 over 10 (9/10)
To me, I believe that a power set is not empty. Here is my thought:
∅ ∊ P(A) where P(A) is the power set and A is the set.
This implies:
∅ ⊆ A
This means that A = ∅, but ∅ ∉ A. ∅ ∊ A if A = {∅} [It makes sense that ∅ ∊ {∅}]. Then, {∅} ⊆ A, so {∅} ∊ P(A) = {∅, {∅}}. That P(A) is not empty since it contains {∅} and ∅.
What is countable set in measure theory?
A countable set is an infinite set that can be put into a one-to one correspondence with the counting numbers. In other words, it is possible to arrange all of the elements of the set in a sequence with a first element, a second element, and so on.
Georg Cantor proved that the rational numbers are countable, but the real numbers are not.
One proof (not Cantor's) that the rationals are countable: Choose any rational number, write it out in its simplest form. Whatever number you wrote is represented by a finitely long string of either the numerals or the division slash (possibly preceded the negative sign). If you consider a base-eleven number system with the division slash as the eleventh numeral, then whatever rational number you just wrote out corresponds directly and unambiguously to one specific integer. Since there exists a mapping scheme that assigns any arbitrary rational number to a specific integer, the rational numbers are countable.
How does the slope affect the steepness of a line?
The larger the absolute value of the slope if, the more vertical, or steeper, the line is. A horizontal line has slope 0, a line that is just a very little bit steep, might have slope, 1/10, a line that is very steep might have slope 10/1 or 10, or even 1000000 and as that number gets bigger and bigger, the line becomes almost vertical. For practical purposes, the slope, or steepness, of the line can be determined by rise over run, or, with a 0/0 intercept, then y over x, or, y1-y2 over x1-x2.
What does the word integers mean in math?
The integers are the infinite collection of all the natural numbers (including zero): 0, 1, 2, 3, 4,... etc., together with the negatives of the non-zero natural numbers: -1, -2, -3, -4, ...
As a set, the integers are usually denoted by the symbol Z (often in a blackboard font), and written {...-3, -2, -1, 0, 1, 2, 3, ...}.
What is another way to say twelve over twelve?
One would suffice in mathematics, because twelve twelfths of something is a whole.
resolved
Because you may have read the question wrong
How many 1's and 0s can one byte of memory contain?
One byte is commonly accepted as holding eight bits. Therefore, one byte can hold eight 1's or eight 0's or anything in between, such as three 1's and five 0's.
This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if, given any two sets in the collection, those two sets are disjoint.
Formally, let I be an index set, and for each i in I, let Ai be a set. Then the family of sets {Ai : i ∈ I} is pairwise disjoint if for any i and j in I with i ≠ j,
For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {Ai} is a pairwise disjoint collection (containing at least two sets), then clearly its intersection is empty:
However, the converse is not true: the intersection of the collection {{1, 2}, {2, 3}, {3, 1}} is empty, but the collection is not pairwise disjoint. In fact, there are no two disjoint sets in this collection.
A partition of a set X is any collection of non-empty subsets {Ai : i ∈ I} of X such that {Ai} are pairwise disjoint and
Sets that are not the same.
What is the solution to y3x 22 y2x 16 by using systems by substitution?
If you mean (1) y + 3x = 22 and (2) y + 2x = 16, then
(1) y = 22 - 3x (sub this into (2))
(2) (22 - 3x) + 2x = 16
-x = -6
x = 6
y = 22 - 3x = 22 -3(6) = 4
solution: (6,4)
What is the common factor of 12 20 write the sum of the two numbers in factor form?
The common factors of 12 and 20 are 1, 2 and 4.
12 + 20 = 32
The factors of 32 are 1, 2, 4, 8, 16 and 32.
The prime factorization of 32 is 2 x 2 x 2 x 2 x 2 or 25
What is 678 plus y times x times z plus 1 times 12 divided by 12 multiplied by 360?
678 + xyz + 360 = xyz + 1038
78 42 are, as far as I can make out, two numbers. They do not make a triangle.
78 42 are, as far as I can make out, two numbers. They do not make a triangle.
78 42 are, as far as I can make out, two numbers. They do not make a triangle.
78 42 are, as far as I can make out, two numbers. They do not make a triangle.
Is there any shortcut function to match positive amount with Negative amount in Excel 2007?
=-b7
where b7 is an example cell reference. The result will be the negative of whatever is in b7.
Is The value π a rational number?
The symbol for pi is not a rational number because it can't be expressed as a fraction
Simplex is the herpes virus, and type 1 is oral and type 2 is genital.
