Re: 1-1/2+1/3-1/4+1/5-1/6+1/7

Han.deBruijn@xxxxxxxxxxxxxx writes:

Let's repeat the definition of S(). I hope this is the latest version:

y is in S(x) iff there is some n e N such that for all m e N ,
with m > n , y is in S_m(x) .
Here, S_m(x) = s o s o ... o s(x), where there are exactly
m compositions. (m e N)

Lemma ( with () -> [] ) :

y is in S[x] iff there is some n e N such that for all m e N ,
with m > n , y is in S_m[x] .
Here, S_m[x] = s o s o ... o s[x], where there are exactly
m compositions. (m e N)

Proof:

Because S[x] = { S(y) , y e x } and S(y) according to the above.

The proof does not look remotely like a proof of this claim to me.

Let's define

y e T(x) <=> there is an n e N such that for all m e N with m > n,
y is in S_m[x].

You want to claim that T(x)=S[x]. Of course, you've noticed that

S[N] = {N} and
T(N) = {},

so this will yield a contradiction. But your "proof" is not a proof
at all, so let's see what we can do.

S[x] = { S(z) | z in x }
= { y | (E z in x)(E n in N)(A m in N)(m > n -> y in S_m(z)) }

I do not see why that should be the same set as

T(x) = { y | (E n in N)(A m in N)(m > n -> (E z in x)(y in S_m(z))) }

So, you have to show that

(E z in x)(E n in N)(A m in N)(m > n -> y in S_m(z))

iff

(E n in N)(A m in N)(m > n -> (E z in x)(y in S_m(z)))

I don't believe it's so.

--
"My personal opinion is, it was a shameful act for someone to disclose
this very important program in a time of war. The fact that we're
discussing this program is helping the enemy."
-- George W. Bush: Questioning Illegal Wiretaps Just Helps The Enemy!
.

Relevant Pages

  • Re: The Macintosh is a girls computer!
    ... Section 4.3 and the `Bat Bomb' is what I was thinking of - but you ... IFF was first deployed during the Second World War. ... Because IFF is an active system that the enemy can trace. ... In fact it made it very much easier for the German radio ...
    (uk.comp.sys.mac)
  • Re: Railgun Research: Barrrel Design or Power Supply
    ... > that the risk of having all your missiles rendered ineffective if the ... > enemy can mimic your IFF signal isn't worth the benefit of eliminating ... > IFF only works well if you can change your codes faster than the enemy can ... > to base where the codes can be changed. ...
    (sci.military.moderated)
  • Re: Railgun Research: Barrrel Design or Power Supply
    ... > that the risk of having all your missiles rendered ineffective if the ... > enemy can mimic your IFF signal isn't worth the benefit of eliminating ... > IFF only works well if you can change your codes faster than the enemy can ... > to base where the codes can be changed. ...
    (sci.physics)
  • Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
    ... y is in Siff there is some n e N such that for all m e N, ... m compositions. ... Here are the relevant definitions ... hope I don't make another stupid error. ...
    (sci.math)
  • Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
    ... Am I allowed to hook in here, with one of my small but certain steps? ... Let's repeat the definition of S. ... y is in Siff there is some n e N such that for all m e N, ... m compositions. ...
    (sci.math)