Proofs

No such proof can exist within consistent axioms - to add 1 to Graham's number would generate a larger number, and so, by this counterexample, Graham's number cannot be the largest.

It is the largest used in a mathematical proof, because all proofs have been noted in a proof 'by exhaustion', in which all cases (in this case, proofs) have been verified to have smaller constants .

Archimedes made many things. He made (invented) the Archimedes screw which helps farmers with their irrigation. He also supposedly made Archimedes Death Ray (which is a myth) and Archimedes Claw which is said unrealistic by modern engineers.

Removing the barriers of free trade almost always requires a trade treaty. One that is in place in the US is the North American Free Trade Agreement between the US, Canada, and Mexico.

Hi,

A collection of data means too many data files kept on one place. A software will help to do this easily.

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By making it an electromagnet. Include it in a circuit.

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The earth does not have a perimeter. The Perimeter is the distance around a circle. The earth is not a circle, but a sphere (sort of). The measurement around the earth is the circumference. Because the earth is not a perfect sphere, the circumference is different depending on whether you measure it horizontally (the equator) or vertically through the poles (Meridian).

Asa /sss

Algebraically if we have a number 'x^2'

Then its square is (x^2)^2 = x^4

For the square root of x^2 = +/-x

100 can be expressed as the sum of two primes in 6 different ways (ignoring order):

100 = 3+97 = 11+89 = 17+83 = 29+71 = 41+59 = 47+53

0 or 1

Yes, and here's the proof:

Let's start out with the basic inequality 4 < 7 < 9.

Now, we'll take the square root of this inequality:

2 < √7 < 3.

If you subtract all numbers by 2, you get:

0 < √7 - 2 < 1.

If √7 is rational, then it can be expressed as a fraction of two integers, m/n. This next part is the only remotely tricky part of this proof, so pay attention. We're going to assume that m/n is in its most reduced form; i.e., that the value for n is the smallest it can be and still be able to represent √7. Therefore, √7n must be an integer, and n must be the smallest multiple of √7 to make this true. If you don't understand this part, read it again, because this is the heart of the proof.

Now, we're going to multiply √7n by (√7 - 2). This gives 7n - 2√7n. Well, 7n is an integer, and, as we explained above, √7n is also an integer; therefore, 7n - 2√7n is an integer as well. We're going to rearrange this expression to (√7n - 2n)√7, and then set the term (√7n - 2n) equal to p, for simplicity. This gives us the expression √7p, which is equal to 7n - 2√7n, and is an integer.

Remember, from above, that 0 < √7 - 2 < 1.

If we multiply this inequality by n, we get 0 < √7n - 2n < n, or, from what we defined above, 0 < p < n. This means that p < n and thus √7p < √7n. We've already determined that both √7p and √7n are integers, but recall that we said n was the smallest multiple of √7 to yield an integer value. Thus, √7p < √7n is a contradiction; therefore √7 can't be rational, and so must be irrational.

Q.E.D.

It is 1/4.

It is Equal to 104. :-)

They all relate by adding up the 6+6+3=15 You can not get to the sum of 15 is you don't have the first 3 numbers to add up.

Area of a rectangle = length * width = 72 feet-squared

1 verticie oxygen oxygen

It can be rounded to 17,000

To conclude, or deduce, as in, "from the fact that the triangle is equilateral, and the fact that a triangle is isoceles if and only if the base angles are equal, we can infer that it is also equiangular."

I would say so. They are soft enough to eat. Stay away from hard candies and taffy though.

Rectangular bases are congruent to each other. The five other faces connect those bases and are adjacent to each other and the parallel bases to each other. Congruency does not occur on the five equal side shapes. This occurs in odd face prisms. The angle created by the five faces have only partial reflection of each other where as the pentagonal bases are parallel. The reflection on the parallel sides create an optical illusion of bending light.

In a four sided prism however all faces are congruent. A cubed prism would be a perfect congruent prism.

Answer: A regular quadrilateral is one with equal sides and equal angles, so it is a square. To negate this definition, we say an irregular quadrilateral is one where the sides are unequal or the angles are unequal OR BOTH. In simpler terms, we could say it is a quadrilateral which is not a square.

These are exists in d-orbitals only.

"e" refers to doubly degenerate orbitals.It consists of two d-orbitals.

"t" refers to triply degenerate levels orbitals. It consists of three d-orbitals. Degenerate means having same energy. They derive from group theory.

The "g" tells you that the orbitals are gerade (german for even) - they have the same symmetry with respect to the inversion centre.