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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
I presume you mean intersecting. Two sets are intersecting if they have members in common. The set of members common to two (or more) sets is called the intersection of those sets. If two sets have no members in common, their intersection is the empty set. In this case the sets are called disjoint.
How long would it take to spend 1 million dollars if you spend 1000 each day?
Well let's think about this.
1,000,000 / 1,000 gives 1,000 or about 2.73791 years.
What is the divisibility rules of 105?
For a number to be divisible by 105 it must be divisible by 3, by 5 and by 7. So, divisibility by 3 requires all three of the following to be satisfied:
- Sum the digits together. Repeat if necessary. If the answer is 0, 3, 6 or 9 the original number is divisible by 3.
- If the final digit of the number is 0 or 5, the original number is divisible by 5.
- Take the number formed by all but the last digit. From it subtract double the last digit. Keep going until there is only one digit left. If it is 0 or 7 then the original number is divisible by 7.
Does 6.66 equal 6 hours 46 minutes?
6.66 hours is 6 hours 39 minutes 36 seconds.
6.66 repeating is 6 hours 40 minutes.
Complex analysis is a metric space so neighborhoods can be described as open balls. Proof follows
a. Assume that the set has an accumulation point call it P.
b. An accumulation point is defined as a point in which every neighborhood (open ball) around P contains a point in the set other than P.
c. Since P is an accumulation point, I can choose an open ball around P that has a diameter less than the minimum distance between P and all elements of the finite set. Therefore there exists a neighbor hood around P which contains only P. Therefore P is not an accumulation point.
How many ways can the word Tennessee be arranged?
Well, there are 9 letters in Tennessee, and, based on the question, you can only use each letter once.
The first letter has 9 possible outcomes.
The second letter only has 8, because you have already used one.
The third would have 7, etc.
9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 322,880
How many pieces of A4 fit into A1?
A4*2 = A3
A3*2 = A2 = 2*2*A4
A2*2 = A1 = 2*2*2*A4 = 8*A4
Answer: 8 pieces of A4 zized papers will fit on 1 sheet of A1.
What is the fourier transform of Tan function?
tanx = 2*(sin2x - sin4x + sin6x - ... )
However, be warned that this series is very slow to converge.
What is the use of studying theory of computation?
There are several uses. I will mention two.
One is to make calculations more efficient. For example, suppose you want to calculate x^2 + 2x + 4. Each operation is binary, that is, two inputs are converted to one output.
Option I
- calculate x*x
- calculate 2*x
- add them together = x*x + 2*x
- add 4 to the above.
or
Option II
- calculate x+2
- multiply by the above by x = x^2 + 2x
- add 4 to the above.
That saves 1 binary operation in the calculation. If such a calculation is carried out thousands - or millions - of times, this small difference can save a lot of time.
Second, it is important to understand the behaviour of computation errors. Most rational numbers and all irrationals have infinitely long decimal - or binary - representations. Computers cannot work with infinitely long strings of digits and so need to truncate the numbers. This leads to rounding errors and understanding these is crucial in understanding the accuracy and limitations of your calculations.
Why is anything divided by zero equal to infinity?
Division by zero is undefined. Even dividing zero by zero is undefined. That's because there are no unique results. This derives from the identity function of zero, such that any value multiplied by zero is zero.
While the division of any number by a diminishing fraction has a limit of infinity, there is no reverse operation possible. I.e. for any nonzero number n:
If n/0 = ∞ it implies ∞ x 0 = n but any number times 0 = 0
and
If 0/0 = n then n could be any real number, not just 1, because n x 0 = 0
What kind of statement has the form of 'if A then B' which means if a is true then b must be true?
An example of a conditional statement is: If I throw this ball into the air, it will come down.
In "if A then B", A is the antecedent, and B is the consequent.
What number is halfway between 0 and 0.01?
The number halfway between 0 and 0.01 is (0+0.01)/2 = 0.005
What is the sample space when flipping a coin?
The sample space when flipping a coin is [heads, tails].
How many strings of three decimal digits do not contain the same digit three times?
Probably 990, depending on the rules.
Fun question, but there is more than one answer depending on the rules. If the first digit can be zero, and if you can accept 001, 002, etcetera as answers, then you have 10 choices for the first digit, 10 choices for the second digit, and 10 choices for the third digit. But, you have to subtract the ten occurrences when all three digits match (000, 111, 222, 333, etc.) 10 x 10 x 10 - 10 = 990.
Why we use sine angle in cross product while cos angle in dot product?
Because in dot product we take projection fashion and that is why we used cos and similar in cross product we used sin
