- #1

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Why couldn't i just line up all the decimal numbers with the the odd natural numbers.

Then when we create a new decimal that is on my list I will line it up with an even number because I haven't used any of those yet.

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- Thread starter cragar
- Start date

- #1

- 2,552

- 3

Why couldn't i just line up all the decimal numbers with the the odd natural numbers.

Then when we create a new decimal that is on my list I will line it up with an even number because I haven't used any of those yet.

- #2

HallsofIvy

Science Advisor

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- #3

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Why couldn't i just line up all the decimal numbers with the the odd natural numbers.

Why do you think you can even do that?? You can't. That's the whole point of the diagonal argument, you can't line up all the decimal numbers with the odd natural numbers.

The diagonal argument is a proof by contradiction.

- #4

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just saying we will start with that, then the new number that you create that is not on

my list I will line that one up with an even number and the next decimal you line

up with the next even number. I could do that with the rational numbers

I could line up the naturals with the naturals and then create a rational that wasn't on my list but we know that the rationals are countable so it is not clear to me why the diagonal argument works now.

- #5

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- #6

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powers of primes to line up with the new numbers that you create that aren't on my list .

It just isn't clear to me.

- #7

- 22,129

- 3,298

powers of primes to line up with the new numbers that you create that aren't on my list .

It just isn't clear to me.

So that way you won't find a contradiction.

But the usual way, you do find a contradiction.

It's not because you can't find a contradiction if you do something different, that the diagonal argument doesn't work.

- #8

lurflurf

Homework Helper

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like this

1 has egg

2 does not have mayo

3 does not have onion

4 has pickle

5 has worms

6 has orange peel

7 has yak cheese

8 does not have rhubarb

...

To make a new sandwich switch the option given for each existing sandwich. Since the sandwich differs from each existing sandwich in at least one option, it must be new.

- #9

lavinia

Science Advisor

Gold Member

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powers of primes to line up with the new numbers that you create that aren't on my list .

It just isn't clear to me.

You can't line up the reals with the powers of 5 or the odd numbers ot any subset of the integers. You are assuming what you want to disprove.

- #10

Hurkyl

Staff Emeritus

Science Advisor

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Once we've made infinitely many choices to fill up your list completely, I'm going to apply the diagonal argument again to produce yet another number not on your list.

powers of primes to line up with the new numbers that you create that aren't on my list .

It just isn't clear to me.

Since your list is full, there's no room for you to add this new number to the list.

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