Question

Theoreticals of Calculus: Let R be the relation on N(atural numbers) given by xRy iff x divides y.

Answer 1

The answer is in the pdf pg 10. number 6.11 a)

Answer 2

The question is asking if it is symmetric and or reflexive

Answer 3

i understand why it is reflexive but why not symmetric? i thought the question was saying the relation is only if x and y can divide with each other, not that they are equal to the same value

Answer 4

to be symmetric means:

\[a\div b ~therefore~b\div a \]

right?

Answer 5

yes

Answer 6

can you think of 2 natural numbers x,y such that:

\[x\div y\ne y\div x\]

Answer 7

well if x = 1 and y = 2, but the way the question was worded, i was thinking that they don't have to equal each other, they just have to be able to divide and become a rational number. is the x --> y then y --> x mean that both answers are the same or equal?

Answer 8

the not equals sign is prolly a bad choice

Answer 9

the relation is on the natural set, not the rational set right? or am i seeing that off?

Answer 10

your right, oh so that means that the numbers inputted and outputted must be natural numbers

Answer 11

i believe so, im not up to par on the terminology tho -- that "relation on N" part :)

i do believe it means that we have to be closed under the operation tho

Answer 12

oh ok, so why is there the transitive property which states that "if xRy and yRz, then xRz"?

Answer 13

oh do you know for sure it has transitive property?

Answer 14

if y|x, then for some integer n; x = yn

Answer 15

if y|x and z|y then

x = yn

y = zm

x = z(mn); therefore z|x is transitive

Answer 16

hmm ok that makes sense! Thank you ^_^

Answer 17

yore welcome, good luck :)

Answer 18

thanks!