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Anonymous Tue 23 Feb 10:04:54 2021 No.12745085 View Reply Original Report

Quoted By: >>12747523

why is set theory notation so confusing?

Anonymous

Anonymous Tue 23 Feb 2021 10:08:20 No.12745094 Report

Quoted By: >>12745110

i can't imagine what's confusing about it. what are you having trouble with?

Anonymous

Anonymous Tue 23 Feb 2021 10:18:02 No.12745110 Report

Quoted By: >>12745122

>>12745094
what is the difference between
$\{1,2}^\mathbf{N}$
and
$\{a,b}^\mathbf{N}$

Anonymous

Anonymous Tue 23 Feb 2021 10:21:21 No.12745122 Report

Quoted By: >>12745154 >>12745169

>>12745110
$\{a,b\}^\mathbf{N}$
$\{1,2\}^\mathbf{N}$

Anonymous

Anonymous Tue 23 Feb 2021 10:37:42 No.12745154 Report

Quoted By: >>12745162 >>12745194

>>12745122
i've never seen that notation. what does the raised N mean? are you trying to indicate a cartesian product or something?

Anonymous

Anonymous Tue 23 Feb 2021 10:41:47 No.12745162 Report

Quoted By: >>12745171

>>12745154
set of all functions N -> {a,b}

Anonymous

Anonymous Tue 23 Feb 2021 10:47:21 No.12745169 Report

Quoted By: >>12745171 >>12745184

>>12745122
They're isomorphic

Anonymous

Anonymous Tue 23 Feb 2021 10:48:50 No.12745171 Report

Quoted By: >>12745184

>>12745162
assuming N is natural numbers, essentially it seems like this is shorthand for "all countably infinite strings built from an alphabet of 2 symbols."

>>12745169
what he said

Anonymous

Anonymous Tue 23 Feb 2021 10:54:39 No.12745184 Report

Quoted By:

>>12745169
>>12745171
I see, thanks

Anonymous

Anonymous Tue 23 Feb 2021 10:56:59 No.12745194 Report

Quoted By:

>>12745154
thinking about it more, it is a cartesian product of the form
$<br />\times_{i=0}^{\infty} \{1,2 \}<br />$
which is equal to the set of all infinite strings consisting of 1s and 2s
i like this notation more, but can see the point of your notation

Anonymous

Anonymous Tue 23 Feb 2021 11:02:17 No.12745204 Report

Quoted By:

to be clear
$\{1,2\} = \{1,2\}$ $\{1,2\} \times \{1, 2\} = \{ (1,1), (1,2), (2,1), (2,2)\}$ $\{1,2\} \times \{1, 2\} \times \{1, 2\}= \{ (1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2), (2,2,1), (2,2,2)\}$
and so on
you get why they use an exponent like notation
note, i've taken the liberty of collapsing the ordered pairs i.e. ((1,1),1) = (1,1,1)

Anonymous

Anonymous Tue 23 Feb 2021 17:35:57 No.12746262 Report

Quoted By: >>12746942

>is 0?N ?
>"uhhhhh only when it's not a trivial answer"
why are they like this?

Anonymous

Anonymous Tue 23 Feb 2021 21:13:52 No.12746942 Report

Quoted By:

>>12746262
it really doesn't matter. that's why there has never been a consensus on the definition, unlike other definitions like 0! = 1 which seems to greatly simplify a lot of important math

Anonymous

Anonymous Tue 23 Feb 2021 23:59:02 No.12747523 Report

Quoted By:

>>12745085
who are these nice little buddies in the picture

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