0
No Q is not cyclic under addition.
Wiki User
∙ 13y ago
Add your answer:
Earn +20 pts
Is 2.3333..... irrational or rational?
It is rational.Any number that has a digit, or group of digits, that repeat forever is rational.
Is this a rational number 0.131131113?
If you mean to continue the pattern indefinitely, adding more digits, and one more "1" in every cycle, then it is NOT rational. In the case of a rational number, the EXACT SAME group of digits has to repeat over and over (perhaps after some other, initial, digits), for example:0.45113113113113113... Here, the group of digits "113" repeats over and over, so the number is rational.
Show that the sum of rational no with an irrational no is always irrational?
Suppose x is a rational number and y is an irrational number.Let x + y = z, and assume that z is a rational number.The set of rational number is a group.This implies that since x is rational, -x is rational [invertibility].Then, since z and -x are rational, z - x must be rational [closure].But z - x = y which implies that y is rational.That contradicts the fact that y is an irrational number. The contradiction implies that the assumption [that z is rational] is incorrect.Thus, the sum of a rational number x and an irrational number y cannot be rational.
How do you know if a decimal is rational or irrational?
A decimal is rational if it:either ends and doesn't go on forever; ORit is a repeating decimal.A decimal is irrational if it goes on forever and ever and never stops without repeating.The number: 5.77777777 is rational because it goes on forever, REPEATING the same number (the digit 7).It can also repeat a group of numbers, like the number: 8.789789789789789789See how the "789" is REPEATING over and over again and never stops? That is a rational decimal!
The discovery of what element led to the addition of group zero?
The discovery of the noble gases led to the addition of the group 0, which is also designated as group 18/VIIIA.
Is it true that an infinite cyclic group may have 3 distinct generators?
A cyclic group, by definition, has only one generator. An example of an infinite cyclic group is the integers with addition. This group is generated by 1.
Why does every rational number have a additive inverse?
The rational numbers form an algebraic structure with respect to addition and this structure is called a group. And it is the property of a group that every element in it has an additive inverse.
Are rational numbers under addition a group?
Yes.
Every subgroup of a cyclic group is cyclic?
Yes, every subgroup of a cyclic group is cyclic because every subgroup is a group.
What is the order of the cyclic group mean?
The order of a cyclic group is the number of distinct elements in the group. It is also the smallest power, k, such that xk = i for all elements x in the group (i is the identity).
Is every abelian group is cyclic or not and why?
every abelian group is not cyclic. e.g, set of (Q,+) it is an abelian group but not cyclic.
What is a group of rational numbers?
A rational number is a number that can be expressed in fractional form.
Is 2.3333..... irrational or rational?
It is rational.Any number that has a digit, or group of digits, that repeat forever is rational.
How do you determine number of isomorphic groups of order 10?
There are two: the cyclic group (C10) and the dihedral group (D10).
Do positive rational numbers form group?
Yes, with respect to multiplication but not with respect to addition.
What is finite and infinite cyclic group?
Normally, a cyclic group is defined as a set of numbers generated by repeated use of an operator on a single element which is called the generator and is denoted by g.If the operation is multiplicative then the elements are g0, g1, g2, ...Such a group may be finite or infinite. If for some integer k, gk = g0 then the cyclic group is finite, of order k. If there is no such k, then it is infinite - and is isomorphic to Z(integers) with the operation being addition.
How can closure property help understand the type of solution you might expect with operations?
In a group with closure the solution to the operation must be a number from the same set. The set of integers and the set of rational numbers are closed under addition. So the sum of two (or more) integers must be an integer, the sum of rational numbers must be a rational number.
