Inductive Proof for use as proposition in paper

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Homework Statement


Model the concept of space time using Set Theory



Homework Equations


Discrete Mathematics
Logic
Set Theory


The Attempt at a Solution


Try 1
Proposition X

The subset T is the set of ordered space time.
The point of space time s is in T
If s is in T then so are s-1 and s-2
Only sequences so formed are in T.

T={s:s s-n,...,s-2,s-1,s,s+1,s+2,...,s+n}
The set T contains all of space time such that s is an element of T?
 
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Papa Joe says I need to change the title to say "inductive definition" not proof. We are to define the frames that will have to be rendered, not prove anything ;-)
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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