Counting is the process of determining the number of elements of a finite set of objects. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the same element more than once, until no unmarked elements are left; if the counter was set to one after the first object, the value after visiting the final object gives the desired number of elements. The related term enumeration refers to uniquely identifying the elements of a finite (combinatorial) set or infinite set by assigning a number to each element.
Counting sometimes involves numbers other than one; for example, when counting money, counting out change, "counting by twos" (2, 4, 6, 8, 10, 12, ...), or "counting by fives" (5, 10, 15, 20, 25, ...).
There is archaeological evidence suggesting that humans have been counting for at least 50,000 years. Counting was primarily used by ancient cultures to keep track of social and economic data such as the number of group members, prey animals, property, or debts (that is, accountancy). Notched bones were also found in the Border Caves in South Africa that may suggest that the concept of counting was known to humans as far back as 44,000 BCE. The development of counting led to the development of mathematical notation, numeral systems, and writing.
Hexadecimal numbers are made using the sixteen digits 0 - 9, A-F. how many hexadecimal numbers are there between the hexadecimal numbers 30 and AF?
There are 8 numbers between 3 and A, so I got 3 x 16, but I don't really know.
I can't seem to put the Fundamentals of Counting to good use... I have such a hard time answering probability questions with the rules of counting. Here's one question that blew my mind:
There are 4 persons. The sample space E consists of the events E={E1, E2, E3, E4, E5 }. Let E1 be the...
in this postcrpit i would like to say i have fund a second order integral equation (fredholm type) for the prime number counting function in particular for Pi(2^t)/2^2t function being Pi(t) the prime number counting function,teh equation is like this is we call Pi(2^t)/2^2t=g(t) then we have...
Here's an old one: starting with 0 (or 1) list all the natural numbers using nothing but 4 4s. I'll go first.
0 = (4 - 4)/(4*4)
1 = (4*4)/(4*4)
2 = (4*4)/(4*sqrt(4))
... etc
The question is how many 8-bit strings have either the second or the fourth bit 1 (or both)?
I know the soulution is 3*2^6 but why??
Also this question how many 8 bit strings begin and end with 1? is it 8C2?
Having a lot of trouble with this problem as well:
How many integers less than 500 are relatively prime to 500?
I know that when two numbers are relatively prime, that means that the greatest common divisor of those two numbers is 1. But I can't figure out a formula that uses sets in order...
I have some questions about counting principles in mathematics:
If I had standard deck of 52 playing cards, then
a. How many ways can one draw a heart or a spade?
b. " " an ace or a king?
c. " " a card numbered 2 through 10?
d. " " a card numbered 2 through 10 or a king?
I got these answers...
I think i got this answer.
How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?
Wouldn't the answer just be C(5,3) because the boxes are indistinguishable? Or do i treat this question the same as if the boxes were distinguishable?
A general two digit counting number is:
d1*b + d0 = C ; where C is the count
Let b = 2 as an example
d
1 0 C
------
0 0 0
0 1 1
1 0 2
1 1 3
b is the count of symbols in the digit, but it can start at 0
d1*0 + d0 = C ; works fine
d0 = C ; and can be any base.
d
1 0 C...
The dial on a 3 number combination lock contains markings to represent the numbers from 0 to 59. How many combinations are possible if the first and second numbers differ by 3?
What I did was:
1st number: It can be any of the 60 numbers (if we take 0 also as a #)
2nd number: I think since...
is there an easier way of knowing how to count certain sequences in a problem using the same concept, i mean there are formulas but how do we tell which one we should use.
Hello all! First of all, please excuse me for barging in on you all like this. I am a nobody with little formal education in ANY field and I apologize if I seem a little mad. The bottom line is this - I just CANNOT find any satisfactory answers to my questions across the whole of the net and...