Proofs

It's always a common multiple; it's not always least.

Simple counter example:

4 × 6 = 24

But LCM(4, 6) = 12

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Note: HCF(4, 6) = 2

What is true of any two whole numbers that the product of the two numbers is equal to the product of their highest common factor and lowest common multiple.

eg 4 × 6 = hcf(4, 6) × lcm(4, 6) = 2 × 12 = 24.

No, it could be another asymmetric relation.

the definition of an angle bisector is a line that divides an angle into two equal halves. So you need only invoke the definition to prove something is an angle bisector if you already know that the two angles are congruent.

how to solve Mind Game - Square Off - Dr Wood volume.9

If you are born in 1988 you would be 24 in 2012. To find anyone's age, take the current year and subtract the year that the person was born in.

The value of silver and other metals constantly changes so any answer posted here would be out of date almost immediately. While it's not normal WikiAnswers policy to say "use the Internet", that's the best approach in this case. You can check a site such as www.kitco.com, CNNMoney, etc. for the latest prices.

Such statements are called postulates in geometry and axioms in other areas.

Definitions are also accepted without proof, but technically they are abbreviations rather than statements.

I would do it like this though I'm sure there are other ways:

There are 10 multiples of 3 every 30 (3,6,9,12,15,18,21,24,27,30).

There are (1000/30)= 33 lots of 30 in 1000

Therefore there are (10 x 33)=330 multiples of 3 which brings us up to 990 (330x3 =990)

Then there are 3 more multiples of 3 993, 996,999

This makes the total 333 multiples of three between 1 and 1001

Consult any textbook on Euclidean geometry.

The prime numbers between 40 and 60 are 41, 43, 47, 53 and 59. These sum to 243.

Lusin's theorem says that every measurable function f is a continuous function on nearly all its domain.

It is given that f measurable. This tells us that it is bounded on the complement of some open set of arbitrarily small measure. Now we redefine ƒ to be 0 on this open set. If needed we can assume that ƒ is bounded and therefore integrable.

Now continuous functions are dense in L1([a, b]) so there exists a sequence of continuous functions an tending to ƒ in the L1 norm. If we need to, we can consider a subsequence.
We also assume that an tends to ƒ almost everywhere. Now Egorov's theorem tells us that that an tends to ƒ uniformly except for some open set of arbitrarily small measure. Since uniform limits of continuous functions are continuous, the theorem is proved.

LCM(46, 50, 4) = 2300.

There is really no such thing as a "greatest common multiple" (GCM). Once you find the least common multiple of a set of numbers, you can keep adding the LCM to itself over and over again. Each new number you get will be a common multiple of your set of numbers, but each new number will always be larger than the previous. This means that you can keep adding while the number approaches infinity and you will still never find a greatest multiple.

Negation says you should write the opposite.

So let's take the statement, Today is Monday. The negation is today is NOT monday. Sometimes it is harder.

Say we have the statement, EVERY WikiAnswers.com question is a great questions. The negation is Some questions on WikiAnswers.com are not great questions.

Theorem 8.11 in what book?

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).

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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