Give a recursive definition for the set X of all natural numbers that are one or two more than a multiple of 10. In other words, give a recursive definition for the set {1, 2, 11, 12, 21, 22, 31, 32, ... }.
B1. 1 is in X.
B2. ? is in X.
R. If x is in X, so is x + 10

Question

Give a recursive definition for the set X of all natural numbers that are one or two more than a multiple of 10. In other words, give a recursive definition for the set {1, 2, 11, 12, 21, 22, 31, 32, ... }.
B1.   	 1 is in X.
B2.   	  ? is in X.
R.  	 If x is in X, so is x + 10

amistre64 · Answer

split it into 2 parts .... even and odds

amistre64 · Answer

for some n=1,2,3,4,$$a_{2n}=1+10(n-1)$$$$a_{2n+1}=2+10(n-1)$$

amistre64 · Answer

might have to rewrite those 2n and 2n+1 ... i was thinking of n=0,1,2,3,4, ....

anonymous · Answer

Thanks so much, I see it now that I split it, I was able to solve B1 and R, now I see B2. 2 is in X

amistre64 · Answer

$$a_{2n-1}=a_1+10(n-1)$$$$a_{2n}=a_2+10(n-1)$$$$a_1=1,~a_2=2$$

anonymous · Answer

thanks again for explain it

amistre64 · Answer

youre welcome