Yes.
No. 1 + 3 = 4, which is not odd. In fact, no pair of odds sums to an odd. So the set is not closed under addition.
Closed sets and open sets, or finite and infinite sets.
Different sets of numbers have different properties. For example,The set of counting numbers is closed under addition but not under subtraction.The set of integers is closed under addition, subtraction and multiplication but not under division.Rational numbers are closed under all four basic operations of arithmetic, but not for square roots.A set S is "closed" with respect to operation # if whenever x and y are any two elements of S, then x#y is also in S. y = 0 is excluded for division.So, the answer depends on what you mean by "number".
Yes.
Yes.
No. 1 + 3 = 4, which is not odd. In fact, no pair of odds sums to an odd. So the set is not closed under addition.
None of the following sets would.
Because there are too many possibilities for the open covering. For a compact set, any family of open sets that covers can be replaced by a finite subfamily of open sets that still covers. Hence the open sets can't be too small. Without compactness, the open sets can be quite small. For example, the infinite family of intervals (1/(n+1), 1/(n-1)) covers the open bounded set (0,1). (Here n is any integer larger than 1.) No subfamily will cover (0,1), and since the sets have radius going to zero, the Lebesgue number would also have to be zero.
Closed sets and open sets, or finite and infinite sets.
From AAA math:Numbers, such as 495,784, have six digits. Each digit is a different place value.The first digit is called the hundred thousands' place. It tells you how many sets of one hundred thousand are in the number. The number 495,784 has four hundred thousands.The second digit is the ten thousands' place. In this number there are nine ten thousands in addition to the four hundred thousands.The third digit is the one thousands' place which is five in this example. Therefore there are four sets of one hundred thousand, nine sets of ten thousand, and five sets of one thousand in the number 495,784.The fourth digit is called the hundreds' place. It tells how many sets of one hundred are in the number. The number 495,784 has seven hundreds in addition to the thousands.The next digit is the tens' place. This number has are eight tens in addition to the four hundred thousands, nine ten thousands, five thousands and seven hundreds.The last or right digit is the ones' place which is four in this example. Therefore there are four sets of one hundred thousand, nine sets of ten thousand, five sets of one thousand, seven sets of one hundred, eight sets of ten, and four ones in the number 495,784.
When you combine any two numbers in a set the result is also in that set. e.g. The set of whole numbers is closed with respect to addition, subtraction and multiplication. i.e. when you add, subtract or multiply two numbers the answer will always be a whole number. But the set of whole numbers is NOT closed with respect to division as the answer is not always a whole number e.g. 7÷5=1.4 The answer is not a whole number.
Different sets of numbers have different properties. For example,The set of counting numbers is closed under addition but not under subtraction.The set of integers is closed under addition, subtraction and multiplication but not under division.Rational numbers are closed under all four basic operations of arithmetic, but not for square roots.A set S is "closed" with respect to operation # if whenever x and y are any two elements of S, then x#y is also in S. y = 0 is excluded for division.So, the answer depends on what you mean by "number".
There are infinitely many sets: Under addition: {1,1,1,1,351}, {1,1,1,2,350}, and so on. {1,2,2,2,348}, {1,2,2,2,347} etc There can also be negative numbers. {-1,1,1,1,353}, {-1,1,1,2,352} and so on. The fraction. Irrational numbers. And these are only sets for addition. Multiplications will bring another infinite set of solutions.
Closed sets and open sets, or finite and infinite sets.
Closed sets and open sets, or finite and infinite sets.
Yes.