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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

Is a square a perpendicular or not?

The segments of a square are perpendicular.

Take the letter " T " for example.

Where the bottom line connects the the top line forms a 90 degree angle, which makes them two lines perpendicular.

What does the word decreased by mean in an operation in math?

There is > and + is all i know

Subtraction: 50 decreased by 10 is the same as 50 - 10.

Give two reason for the set of odd integers is not a group?

Assuming that the question is in the context of the operation "addition",

The set of odd numbers is not closed under addition. That is to say, if x and y are members of the set (x and y are odd) then x+y not odd and so not a member of the set.

There is no identity element in the group such that x+i = i+x = x for all x in the group. The identity element under addition of integers is zero which is not a member of the set of odd numbers.

Is a km bigger or mi?

I'm not sure but I believe a km is bigger than a mi

Which set is a subset of every set?

The empty set is a subset of all sets. No other sets have this property.

How many 16 x 16 patio pavers are needed to make a 12 x 12 stone patio?

81 pavers (each 16 inches square) would be needed.

12 foot x 12 foot = 144 inches x 144 inches = 20,736 in2

16 inches x 16 inches = 256 in2

20,736/256 = 81

What is a binomial factor?

Binomials are algebraic expressions of the sum or difference of two terms. Some binomials can be broken down into factors. One example of this is the "difference between two squares" where the binomial a2 - b2 can be factored into (a - b)(a + b)

Does a steep line always have a negative slope?

A line doesn't have a negative slope if it's steep or not. Possitive and negative slope is determined by the way it goes up or down. When you look at a line from the left to the right, if it gets higher as you get closer to the right, then it has a positive slope. On the other hand, if you also look at it from left to right and the line goes down as it nears the right side, it has a negative slope. If the line is horizontal, it has a slope of 0. If the line is vertical, it has no slope.

Can a function have a limit at every x-value in its domain?

Yes, that happens with any continuous function. The limit is equal to the function value in this case.

Yes, that happens with any continuous function. The limit is equal to the function value in this case.

Yes, that happens with any continuous function. The limit is equal to the function value in this case.

Yes, that happens with any continuous function. The limit is equal to the function value in this case.

Is every cauchy sequence is convergent?

Every convergent sequence is Cauchy. Every Cauchy sequence in Rk is convergent, but this is not true in general, for example within S= {x:x€R, x>0} the Cauchy sequence (1/n) has no limit in s since 0 is not a member of S.

What are the uses of truth table?

A truth table has one column for each input variable (for example, P and Q), and one final column showing all of the possible results of the logical operation that the table represents (for example, P XOR Q). Each row of the truth table contains one possible configuration of the input variables (for instance, P=true Q=false), and the result of the operation for those values. Truth tables can be used to prove many other logical equivalences. Truth tables are also used to specify the function of hardware look-up tables (LUTs) in digital logic circuitry. For an n-input LUT, the truth table will have 2^nvalues (or rows in the above tabular format), completely specifying a boolean function for the LUT. By representing each boolean value as a bit in a binary number, truth table values can be efficiently encoded as integer values in electronic design automation (EDA) software. For example, a 32-bit integer can encode the truth table for a LUT with up to 5 inputs. Truth tables are a simple and straightforward way to encode boolean functions, however, given the exponential growth in size as the number of inputs increase, they are not suitable for functions with a large number of inputs. Other representations which are more memory efficient are text equations and binary decision diagrams.

Is zero divided by ten equals zero?

Yes, zero divided by ten does equal zero. When zero is divided by any number, the result is zero.

What are two prime numbers whose sum is 42?

Split the number in half and make an equation adding the two together to make the desired amount. Unless the number that is half the total is prime, adjust the first number down by an amount to make it a prime number, then adjust the second one up by an equal amount and check whether it is also a prime number. If the second number is also a prime number, you have found two prime numbers that equal the desired amount. If not, adjust the first number down to another prime number, repeating the procedure above until you have two prime numbers.

If you split 42 in half, the result is 21. Take the equation 21 + 21 = 42. Since 21 is not prime, adjust the first number down to 19 which is the first prime number below 21. That means the other number would be 23, which is prime. So, you have two prime numbers that add up to 42 = 19 + 23.
The prime factorization of 42 is 2 x 3 x 7, so it has three factors that are prime: 2, 3, and 7.

A is a ray that divides an angle into two congruent angles?

The answer to that is a bisector. The two angles formed by this has the same angle.

Is a set of isolated points a closed set?

Take the set of points 1/n for all integers n. This is an isolated set of points- that is, for any of them there is an open ball about the point not containing any other point. However, this set has a limit point which is not contained in the set (namely 0), hence it is not closed.

What is seven divided by zero?

truthfully if your stupid the answer is 0 7 times what equal o and its zero dummy.

+++

You can't divide anything by 0.