Re: Cardnality of integers > Cardnality of integers

In article <0cdf751a-07a0-4877-9be0-0b3d88708116@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<S_Paske@xxxxxxxxxxx> wrote:
On Mar 20, 3:24=A0pm, magi...@xxxxxxxxxxxxxxxxx (Arturo Magidin) wrote:
In article <3717a18c-5c8d-49ea-ba14-2ff810309...@xxxxxxxxxxxxxxxxxxxxxxxxx=
com>,

=A0<S_Pa...@xxxxxxxxxxx> wrote:
On Mar 20, 2:41=3DA0pm, Randy Poe <poespam-t...@xxxxxxxxx> wrote:

=A0 =A0[...]





No there isn't. To see this, consider my argument but keep all
exponents < k.
Now, you can see the truth.
Card(base 2 rationals)<Card(base 3 rationals)
Card(SquareFree Rationals)=3D3DCard(Base 2 Rationals) < Card(Base 3
Rationls)

To see this notice:
=3D2E010101110101
=3D2E100011011001
=3D2E011110011110

Now for each digit that is a 1, 'Cantors construction rule' tries to
map that bit to a position that is allready filled. Thus, it is
impossible to map base 3 rationals to base 2 rationls, just as it is
impossible to map square-free rationals to those that are cube free.

I have proven this.

I see that your grasp of the correct meaning of "prove" is about as
solid as your grasp of the meaning of "conjecture"; piss poor in both
cases...

Look, i know i'm not a mathematician,

Then you should stop pretending you can talk like one.

but I'm right.

About the claim that "it is impossible to map base 3 rationals to base
2 rationals"? No, you are not right.

If you don't
think so, then present your argument.

Really? Fine: I don't care what YOU tried to do in order to obtain the
map, there is a trivial map from the base 3 rationals to the base 2
rationals which is one-to-one and onto. Namely, there is a one-to-one
and onto map from "base 3 rationals" to "base 10 rationals" (base
conversion). And there is a one-to-one and onto map from the "base 10
rationals" to the "base 2 rationals" (base conversion). Since the
composition of one-to-one maps is one-to-one, and the composition of
onto maps is onto, then the composite map is a one-to-one and onto
correspondence between the "base 3 rationals" and the "base 2
rationals". Your claim that it is impossible to map the base 3
rationals to the base 2 rationals is therefore nonsense.

Just because whatever it is YOU tried to do didn't work doesn't mean
there is no way to do it. It just means you don't know what you are
doing.

This proof is extremely simple.

I assume you mean "simple" as in the dictionary definition (say, 4a in
the online Merriam Webster): "lacking in knowledge or expertise;
stupid; mentally retarded.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

.

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