Numbers

That's an infinite list.

It is composite.

If a number can be expressed as a terminating or repeating decimal then it is rational (and conversely). So -3 is rational.

Yes you can G64

To rationalize the units on both sides of the equation, E= -GmM/r, e.g if feet is used as the unit of distance r then the Constant G would have a different value.

3 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

One.

#include<conio.h>

#include<stdio.h>

void main (void)

{

int a,b,c,d;

printf("enter the max limit : ");

scanf("%d",&a);

for(b=1;b<=a;b++)

{

for (c=2;c<b;c++)

{d=b%c;

if (d==0) break;}

if (d!=0) printf("%d\n",b);}

getch();

}

by WAli Ahsan

Ch-007

10.0

23357 is a prime number.

Integers between 100 and 999.

pi is a transcendental number and has an infinite decimal representation. Being infinite, there is no last decimal place. Moreover, unlike 1.3 which goes into an infinitely long repeating pattern, pi does not. So there is no answer to the question.

Since 5 is a prime number, then any number, which is not a multiple of 5, is relatively prime with the number 5. You can determine if a number is a multiple of 5, by looking at the ones place digit. If it is a 0 or 5, and the number itself is not zero, then the number is a multiple of 5.

Yes.

What makes man different from all other animals is mans ability to reason. He is able to distinguish between what is right or wrong, good or evil and he makes a choice for the distinction made by the intellect. As a rational being, he is able to take responsibility for his actions because he knows out of reason and not instinct.

No.

Yes and no. Technically speaking the charge of a subatomic particle such as an electron or proton is always the same, this is why they are called constants. However, the methods that have been employed to determine the actual value of the elementary charge may not be the correct value. This would be due to experimental error, etc.

Let's start out with the basic inequality 1 < 2 < 4.

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

1 < √2 < 2.

If you subtract all numbers by 1, you get:

0 < √2 - 1 < 1.

If √2 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 √2. Therefore, √2n must be an integer, and n must be the smallest multiple of √2 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 √2n by (√2 - 1). This gives 2n - √2n. Well, 2n is an integer, and, as we explained above, √2n is also an integer; therefore, 2n - √2n is an integer as well. We're going to rearrange this expression to (√2n - n)√2 and then set the term (√2n - n) equal to p, for simplicity. This gives us the expression √2p, which is equal to 2n - √2n, and is an integer.

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

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

Q.E.D.

It is: 3

What is the number pyramids

You cannot, since being divided by a number is the same as being multiplied by the reciprocal of that number.

For example, (2/3) / (5/4) = 8/15 and (2/3) * (4/5) = 8/15

The only time that you can be sure is if the result is zero. In that case, the fraction has been multiplied by 0. The reciprocal of 0 does not exist and so the operation could not have been division by 1/0.

Any of its factors which includes itself

The only way to get exactly 7 factors is to raise a prime number to the sixth power - so (using the symbol "^" for power), that would be 2^6, 3^6, 5^6, 7^6, 11^6, etc.

There are infinitely many numbers between 0.6 and 0.8. For example,0.60000000000000000002

0.600000000000000000021

0.6000000000000000000211

0.600000000000000000021101

and so on.