Hi, can you help me with this algebra?

Question

I don't understand these:

1. Is there an identity element for subtraction? That is, is a-b a whole number for all whole numbers a and b? Explain.

2. Is the set of whole numbers closed under subtraction? That is, is a -b a whole number for all whole numbers a and b? Explain.

I don't understand either of these, and it would mean the world to me if you could solve them. 10 points and Five stars to the best answer. Thanx!

Answer 1

closure means if u start off with a type of whole numes then if u do something do u still get whole numbers. if u dont it is not closed.

lets try some expamles. if we sutract any 2 numerbs in teh world do we get a whole number?

first let us define a whole number: it is zero and up

0,1,2,3,4,5,6etc

6-9 = -2 that is not a whole number so whole numbers are not closed under  subtraction.

when a is smaller than b then it is not closed.

Answer 2

Hi Ashley,

Identity Element is a number that when combined mathematically with a 2nd number, results in an answer that is the same as the 2nd number. The Identity Element depends on the operation. For example, take Addition. 0 is the Identity Element because any number "N" + 0 = "N". Likewise, 1 is the Identity element for multiplication because any number "N" x 1 = "N"

(1) The Identity Element for subtraction is "0". For example:

     1 - 0 = 1

     2 - 0 = 2

   100 - 0 = 100

    In all cases, the final answer is same as the number from which 0 was subtracted

(2) First, "Closure" is defined on Wikipedia (http://en.wikipedia.org/wiki/Closure_(ma... as follows, "In mathematics, a set is said to be closed under some operation if the operation on members of the set produces a member of the set"

Second, Wikipedia has 3 definitions of WHOLE numbers (a) Non-negative integers (b) Positive integers and (c) Integers. If you Google for the definition, again, you will see all 3 answers depending on the source: http://www.google.com/search?q=definitio...

If you use definition #a or #b then they are not closed because "non-negative or positive integer minus another non-negative or positive integer is not always equal to a non-negative or positive integer" e.g., 3 - 5 = -2 <-- doesn't fit into the non-negative or positive integer definition.

But if you use the 3rd definition of WHOLE, which says all INTEGERS are whole numbers then any integer minus any other integer is always an integer e.g., 2 - 5 = -3 (all are integers).

So my general answer to question 2 is that it depends on your definition of whole numbers. If this is on a test then I would clearly state my assumption, cite Wikipedia as a reference and then write the appropriate answer.

Did this help? good luck!