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Is the group of all real numbers except 0 under multiplication is an infinite group?
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∙ 11y ago
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∙ 11y ago
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What is a group of related multiplication and division facts that use the same numbers?
array
Do positive rational numbers form group?
Yes, with respect to multiplication but not with respect to addition.
Why can't you find the greatest common multiple in a group of numbers?
You can't find the greatest common multiple in any amount of numbers, the number would be infinite.
How many equivalent fraction can be written for any given fraction?
An infinite number! To create an equivalent fraction the numerator and denominator can be multiplied by any number; one such group of numbers that can be used to create a group of equivalent factions is the counting numbers: {1, 2, 3, 4, ...} - multiply the numerator and denominator of the original fraction by 2, then 3, then 4, etc. This group is infinite in size, therefore there are an infinite number of equivalent fractions that can be written for any given fraction.
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.
What is a group of related multiplication and division facts that use the same numbers?
array
Why the set of rationals does not form a group wrt multiplication?
All the elements in a group must be invertible with respect to the operation. The element 0, which belongs to the set does not have an inverse wrt multiplication.
Do positive rational numbers form group?
Yes, with respect to multiplication but not with respect to addition.
Why are the rational numbers under the operation of multiplication not a group?
I believe it is because 0 does not have an inverse element.
Why can't you find the greatest common multiple in a group of numbers?
You can't find the greatest common multiple in any amount of numbers, the number would be infinite.
Is the set of irrational numbers a group under the operation of multiplication?
No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.
What is the rate in math?
The rate, or rate of change is like an average all except it has to do with the slope of a line instead of a group of numbers. Finding the rate of change is like finding an average except you use the points on the graph instead of numbers in a group.
How many equivalent fraction can be written for any given fraction?
An infinite number! To create an equivalent fraction the numerator and denominator can be multiplied by any number; one such group of numbers that can be used to create a group of equivalent factions is the counting numbers: {1, 2, 3, 4, ...} - multiply the numerator and denominator of the original fraction by 2, then 3, then 4, etc. This group is infinite in size, therefore there are an infinite number of equivalent fractions that can be written for any given fraction.
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.
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.
What means an answer found through multiplication?
When we multiply two numbers, the answer we get is called 'product'. The number of objects in each group is called 'multiplicand,' and the number of such equal groups is called 'multiplier'.
Does the set of even integers form a group under the operation of multiplication?
No. The inverses do not belong to the group.
