
#1
Jul1610, 04:01 PM

P: 860

1. The problem statement, all variables and given/known data
Let m be a natural number. Find the flaw in the statement below. Explain why the statement is not valid, and change one symbol to correct it. "If T is a set of natural numbers such that 1) m [tex]\in[/tex] T and 2) n [tex]\in[/tex] T implies n+1 [tex]\in[/tex] T, then T = {n [tex]\in[/tex] N : n ≥ m} 2. Relevant equations Dunno. 3. The attempt at a solution Part 2) of the if statement tells us that T is an infinite set. I'm not sure exactly how 1) and 2) are connected. Hmmmm ... Help me get started. 



#2
Jul1610, 04:05 PM

Sci Advisor
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P: 25,167

To get started think about this. Is m1 in T?




#3
Jul1610, 04:55 PM

P: 860

T is going to look something like {k, k+1, k+2, ...}, where k≥1 is an integer. That's basically what the second condition tells me. m is some element in T. That's all I know about m. Could m1 be in T? As long as m>k. 



#4
Jul1610, 05:01 PM

Mentor
P: 4,499

Let m be a natural number ...
So is their equation for T correct?




#5
Jul1610, 05:11 PM

Sci Advisor
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P: 25,167




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