# Homework Help: Induction principle homework

1. Jul 16, 2010

### annoymage

S={t$$\in$$Z+ | (3t-200)/2 $$\in$$Z+}

how to i find the element of S, provided some of this theorem:

1. every nonempty set of non negetive integer contains a least element: that is, some integer a in S such that a=<b for all b's belongingmto S

2. if a and b any positive integer, then there exist a positive integer n such that na<b

3. induction principle

from theorem 1. how do i find the least integer??

Last edited: Jul 16, 2010
2. Jul 17, 2010

### Office_Shredder

Staff Emeritus
Re: integers

Your goal is just to find the least element of S? I wouldn't use any of those. Look at the function that describes S... it's increasing with t, so you just want to make it as small as possible

3. Jul 18, 2010

### annoymage

Re: integers

can clarify a bit more,
i don't know how to make it small as possible

4. Jul 19, 2010

### annoymage

Re: integers

help T_T, someone,.. clarify for me. owho

5. Jul 19, 2010

### Staff: Mentor

Re: integers

Graph y = (3/2)t - 100 for t > 0. The graph is a portion of a straight line.

6. Jul 19, 2010

### annoymage

Re: integers

ok, i thought of that, hmm, i'll try to convey my inept attempt

the smallest possible are (3/2)t>100 for y to be positive
t must be even for (3/2)t to me integer,

so,
y=2,t=68
y=5,t=70
y=8,t=72
y=11,t=74

so, S={2n+68 l n$$\in$$Z}

so, i don't need use those above definition(except for induction)

7. Jul 19, 2010

### Staff: Mentor

Re: integers

For what t is (3/2)t - 100 > 0?
For what t in Z+ is the inequality above satisified?