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Is it possible to have in a subset S from the set of Real numbers a finite number of upperbounds and yet have no least upperbound?
Let me rephrase it. You mean take a bounded subset of real numbers, S, and find a subset of all the upperbounds of S, say D, such that sup S is not in D?
If I get you right, then yes.
Take D := {a : a = sup s + n, n is natural and n < 4} so the first element is sup s + 1 > sup s, and the remaining two terms are even larger than the first one.
But I think I got you wrong, go through the Completeness Axiom.
That is for any two set A and B such that for all a in A, b in B, a <= b, and they share a maximum of one element, then there exist at least one number x such that a <= x <= b
In particular, A have a supremum, sup A <= x and B have an infimum inf B > = x
sup A <= inf B if they are equal then they must be x.
What else can I help you with?
Is the set of all common multiples of two given whole numbers is finite?
Yes, that is true.
What is the mathematical proof to show that the number of prime numbers is infinite?
The proof is by contradiction: assume there is a finite number of prime numbers and get a contradiction by requiring a prime that is not one of the finite number of primes. Suppose there are only a finite number of prime numbers. Then there are n of them.; and they can all be listed as: p1, p2, ..., pn in order with there being no possible primes between p(r) and p(r+1) for all 0 < r < n. Consider the number m = p1 × p2 × ... × pn + 1 It is not divisible by any prime p1, p2, ..., pn as there is a remainder of 1. Thus either m is a prime number itself or there is some other prime p (greater than pn) which divides into m. Thus there is a prime which is not in the list p1, p2, ..., pn. But the list p1, p2, ..., pn is supposed to contain all the prime numbers. Thus the assumption that there is a finite number of primes is false; ie there are an infinite number of primes. QED.
G is finite where the number of subgroups in g is finite?
Actually a stronger statement can be made:A group G is finite if and only if the number of its subgroups is finiteLet G be a group. If G is finite there is only a finite number of subsets of G, so clearlya finite number of subgroups.Now suppose G is infinite , let'ssuppose one element has infinite order. The this element generates an infinite cyclicgroup which in turn contains infinitely many subgroups.Now suppose all the subgroups have finite order Take some element of G and let it generate a finite group H. Now take another element of G not in H and let it generate a finite group I. Keep doing this by next picking an element of G not H or I. You can continue this way.
Is there an infinite number of factors?
Each integer has a finite number of factors and an infinite number of multiples.
What is the gcf of all of the numbers in the parttern 12 24 36 48?
GCF(12, 224, 36, 48) = 12. Since it is a finite sequence, it can be continued in infinitely many different ways and so there are rules such that any integer (or fraction) can belong to the pattern.
What finite math?
Finite means to end. So finite math is possible math that has to do with numbers ending; no irrational(unending) numbers. Ex: 2+2=4
What is a finite number?
All real numbers are finite. Infinity is not a number.All real numbers are finite. Infinity is not a number.All real numbers are finite. Infinity is not a number.All real numbers are finite. Infinity is not a number.
Are these numbers finite or infinite 35424956?
Finite.
Is a set of prime numbers an finite set?
Finite, no.
Does whole numbers between -2 and 0 are finite or infinite?
Finite
Use finite in a sentence?
There are a finite number of apartments. Finite numbers may be large or small. There are a finite number of states. The number of molds in my fridge is not exactly finite.
Is something that is finite always countable?
Yes, finite numbers are always countable.
What are sets of finite?
They are numbers that terminate.
Are even numbers finite?
noo
What is finite math?
Finite math is a branch of mathematics that focuses on mathematical concepts that have finite, specific values or elements. It typically includes topics such as logic, set theory, probability, statistics, and linear algebra, which are applied to real-world problems with a limited number of possibilities. Finite math is often used in business, social sciences, and computer science to model practical situations.
Is the set of rational numbers finite?
No; there are infinitely many rational numbers.
What is finite sets?
A finite set is a set that has numbers you can count. Its not like infinite with no end it has an end.
