Question

Can you help me "recursively define" this set?

Answer 1

Give recursive definition for this set:
{m | m=4k-2 for some natural number k} assuming natural #s start from 1

Answer 2

An example with answer is:
The set of all positive even numbers:
\[2 \in X\]
\[a \in X, a + 2 \in X\]

Answer 3

list the first few elements of the set first, then i'll give you a hint.

Answer 4

Well, what the equation is saying
m is an element of m=4k-2, and k begins from 1, therefore,

the set should be

{4(1)-2, 4(2)-2, 4(3)-2....4(k)-2}

Answer 5

{2, 6, 10.....4k-2} I think

Answer 6

But how do I "recursively define"?

Answer 7

i can write 6 = 2 + 4, 10 = 6 + 4, 12 = 10 + 4

Answer 8

i dont know what to do with the hint...D:

Answer 9

can you further explain what I should be doing sirm3d?

Answer 10

My set: {2, 6, 10, 14......4k-2}

Base case:
\[2 \in X\]

Inductive clause:
If x in S, then

Answer 11

the next term is 4 more than the previous term

Answer 12

\[\{a_{n+1}=a_n+4\;|\;a_1=2\,,n=1,2,3,\dots\}\]

Answer 13

Ah I think I get it

Answer 14

So my answer should be:

Base case: \[2 \in X\]
Inductive clause:
\[x \in X, x _{n}+4 \in X\]

Answer 15

wait a sec that doesnt seem right...

Answer 16

\[x_1=2 \in X\]
inductive step
\[x_{n+1}=x_n+4\in X\]

Answer 17

ah ok thanks a million sirm3d