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Proofs
Proof means sufficient evidence to establish the truth of something. It is obtained from deductive reasoning, rather than from empirical arguments. Proof must show that a statement is true in all cases, without a single exception.
1,294 Questions
Are the set of positive integers are equivalent to the set of natural numbers?
N-P = 0.
Note here that N is the set of Natural numbers, P is the set of positive integers, and - is the set operation that in the above statement implies N and P are the same, with the exception that 0 is an element of N but not of P.
Why both inductive and deductive reasoning can be used in maths?
Because both are based on strict rules of logical reasoning.
How thick would be a piece of paper folded 103 times?
Depends how you fold it, but if you fold in such a way that each folding doubles the thickness, that would be 2 to the power 103 times the thickness of a single sheet. (You CAN'T do that with any real paper.)
The first heat transpland was performed in 1991 True or false?
False. Prehistoric cave dwellers used fire and the transfer of heat to keep warm!
Weigh 3 balls at a time. The set of 3 that weighs more will have the heavy ball in it. Now weigh each of those 3 balls one at a time. This method uses the scale 4 or less times, depending on how soon you are able to find the heavy ball.
We cannot assume the ball is heavier.
The answer is 92. Simply add the numbers together arithmetically as you would for the problem two plus two. To check your work, a calculator is the best option.
If the values represent vectors at right angles then the answer is 72.73
There are two concepts for Islam; namely
- Islam in its general sense as full submission to God, the Creator; as the one and only God with no partner, no son, no father, no companion, no associate, and no equivalence. In this sense the first who came up with Islam were Adam and Eve.
- Islam per Quran revelation by God to prophet Muhammad through the angel Gabriel (or Jibril) that started in year 610 AD through 632 AD (year of the prophet Muhammad's death). In this sense, the prophet Muhammad (peace be upon him) is the first who came up with Islam
How dou measure temperature in celsius?
Using a thermometer? Isn't i obvious?
If you mean convert, than you can find formulas online.
If you are using Freniheit, which I can't even spell right, I can tell you it's not practical at all in the field of Science to use it, so find formulas online to convert it.
If you cut off a squarehow many face egdes and verticies does a the new polyhedron have?
A square is not a polyhedron, it is a polygon. A cube is not a polygon, it is a polyhedron.
A square has 4 edges and 4 vertexes. It has no faces because it is not a polyhedron. If you cut the corners off of a square, the new polygon has 8 edges and 8 vertexes.
A cube has 6 faces, 12 edges, and 8 vertexes. If you cut the corners off of a cube, the new polyhedron has 14 faces, 36 edges, and 24 vertexes.
In math what one thing do you need to prove a statement is false?
To prove a statement false, you need ONE example of when it is not true.
To prove it true, you need to show it is ALWAYS true.
20, 70 and 90 degrees.
What is the difference between a ruler postulate and a protractor postulate?
a ruler measures the distance and a protractor measures the angles
Kwan has modeled a number that is?
Kwan has modeled a number that is less than 999. His model has twice as many 100-blocks as 10-blocks. It has twice as many 10-blocks as 1-blocks. What is the number?
Counter example that a positive integer is not equal to the sum of two squares?
3 is the smallest integer that cannot be written as the sum of two squares. This is easy to see, since the only squares less than or equal to 3 are 0 and 1.
Is Polynomial function is a field?
No, it is not. f(x) = 2x + 3 and g(x) = 3x2 are polynomials but f(x)/g(x) is not a polynomial.
How many factors does 1800 have?
The positive integers of 1800 are:
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800
This is a total of 36 positive integer factors.
What are all of the combination of a 3 dice roll?
The ans is 56. http://www.quadibloc.com/other/bo0201.htm http://mathforum.org/library/drmath/view/56115.html
Where can the perpendicular bisectors of the sides of a right triangle intersect?
They meet at the centre of the longest side. (Imagine a rectangle with one diagonal, and then draw the 2 lines which slice the rectangle into 4 equal quarters). So the length of the bisector of the longest side of the triangle is zero.
What is Kepler's universe theory?
well this theory was that the sun was a princaple source of motive power in the universe
First we will assume that sqrt(2) is rational, meaning that it can be written as a ratio of two integers say (p/q) p and q must have no common factors sqrt(2)=p/q, square both sides 2=p^2/q^2, multiply both sides by q^2 2q^2=p^2, since 2 divides by the LHS, so does the RHS, meaning that p^2 is evenand because p^2 is even, so is p itselfLet p=2r with r being an integer so that p^2=2q^2=(2r)^2=4r^ 2Since 2q^2=4r^2, q^2=2r^2Because q^2 is 2r^2, then q^2 is even, meaning q itself is evenSince p and q are even, they have a common factor of 2THEREFORE, sqrt(2) cannot be rational
What is the formula to find the radius of a cone?
You must know some information about the cone, volume and height.
V = (1/3) pi x r2 x h, so substitute those values in, rearrange and solve by taking square root at the end of the problem.
Assume a triangle ABC with a line AB (containing the side AB) with external angle D which is formed when line AB and line segment AC intersect. We are asked to prove that the external angle D is equal to the sum of the two interior angles B and C. Angles A and D are supplementary angles (they sum to 180 degrees) because they are linear angles (both together make a straight line, or a 180 degree angle). This means:
m<A + m<D = 180 degrees.
m<A = 180 deg - m<D
Then because A, B, and C are the three angles in a triange:
m<A + m<B + m<C = 180 deg
m<A = 180 deg - m<B - m<C
By substituting 180 deg - m<D in for m<A in the above equation we get:
180 deg - m<D = 180 deg - m<B - m<C
Subtract 180 deg from each side:
-m<D = -m<B - m<C
Multiply both sides by -1
m<D = m<B + m<C
Which proves that the measure of the external angle D is equal to the sum of the two opposite interior angles B and C for any given triangle.
wow. that's a lot. lol.
How to determine the number of group of order 10 upto isomorphism?
10 = 2*5, a product of 2 primes, and 2 divides (5-1). So there are only two groups.
