find ten rational number between 9/5 & 9/7
Answers
Answer:
u
Step-by-step explanation:
When you are talking about a number, which satisfies one or more conditions, four questions come 1o mind (1) does such a number exist? (2) is it unique ? (3) if it is not unique what is the cardinality (i.e. how many are there of these numbers) (4) how can you explicitly find one of them? (5) how can you find all of them? Now let’s to try to apply these tasks to your question. We are talikmg about a number x such that x > a and x < b, where a = 5/9 and b = 9/10. Question (1) is easy find a possible solution by either adding the numerator and denominators of a and b; this gives 14/19. Or choose x= (a+b)/2; in this case 131/180. (2) no it is not unique; I have already suggested two different answers in this case. (3) you can keep finding more and more numbers in a sequence by taking a value between a and the lowest of the x values you have found already. This sequence can be counted and hence the cardinality is at least the same as the cardinality of the set of natural numbers. It can’t be more than this because the set of possible x values is a subset of the set of all rational numbers. I think (4) and (5) cam be left as easy exercises.
Step-by-step explanation:
36/35,37/35,38/35,39/35,40/35,41/35,42/35,43/35,44/35.