« first day (3571 days earlier)      last day (1202 days later) » 

Martin Sleziak
Martin Sleziak
04:25
This room has been relatively silent recently. Just in case it gets frozen, I will remind that moderators can unfreeze chatrooms - so you can ask some moderator (from any site) whether they would be willing to do so. See also: meta.stackexchange.com/tags/frozen-rooms/info and How do I unfreeze a frozen chat room?
 
2 hours later…
soupless
soupless
06:07
I want to ask something. The set $\{a\}$ has an empty subset $\{\emptyset\}$. The set $B = \{\{a\}\}$ also has an empty subset. If I count the number of subsets, would there be two empty subsets?
Math
Math
@soupless what do you mean what is a?
soupless
soupless
Let's just say it's a real number.
Math
Math
{\empty} is not empty!
the empty set has no elements
{\empty] has an element namely the empty set
soupless
soupless
Wait, $\{\emptyset\}$ has 1 element, and $\emptyset$ is the empty set?
Math
Math
yes
soupless
soupless
06:21
How many empty sets are there in $\{\{a\}\}$? Is it two or one?
I think it should be two since $\{a\}$ has one and \{\{a\}\} can be made into something like $\{b\}$ which also has an empty subset
Math
Math
what do you mean by how many empty sets are there?
in order to answer a question you must first define it properly
soupless
soupless
I am sorry if it is not clear enough.
The set $\{a\}$ has one empty set, right?
Math
Math
what do mean by has one empty set?
soupless
soupless
wait, is $\{a\}$ actually $\{a, \{\emptyset\}\}$?
Math
Math
No of course not.Why would you think that? One has one element the other 2
soupless
soupless
06:32
huh? I thought every set has a subset which is an empty set
Math
Math
do you know the difference between subset and element?
soupless
soupless
wow, i don't know anymore
subset is a part of the set, and elements make up the set, right?
Math
Math
if you use ambiguous definitions then is what will happen
soupless
soupless
i thought subsets can be elements?
Math
Math
see this math.stackexchange.com/questions/131309/…
the empty set is a subset of every set but its not an element of every set!
soupless
soupless
06:49
ok. i think i got it.
there should be two empty sets as subsets?
Math
Math
07:10
@soupless the empty set is unique
soupless
soupless
does this mean that the empty set of $\{a\}$ and $\{\{a\}\}$ is the same?
Math
Math
empty is a subset of both of them
soupless
soupless
ok, i understand now. the empty set of $\{a\}$ also belongs to $\{\{a\}\}$
Math
Math
is a subset of not belongs to
proofwiki.org/wiki/Empty_Set_is_Unique
 
6 hours later…
Math
Math
13:13
@soupless do you understand now?
soupless
soupless
I still don't, unfortunately
Math
Math
13:30
Ok do you undersntd the difference between a subset and a element?
of a set
IF you don't understand this then did you read the Math SE post I linked ?
And if you do can you give a proper definition of a subset ?
soupless
soupless
If $A$ is a subset of $B$, then $a \in B$?
Math
Math
what is a
soupless
soupless
The elements of $A$
Math
Math
13:53
You should say
$A$ is a subset of $B$ means that $\forall x(x\in A \to x\in B)$
Are you familiar with logical quantifiers
And truth tables?
soupless
soupless
The "for all" and "there exists", right?
Math
Math
yes
are you familiar with vacuous truths?
soupless
soupless
No. I am familiar with truth tables but not vacuous truths
Math
Math
Ok if I let A be the empty set and B be any set then what happens?
soupless
soupless
A is a subset of $B$
Math
Math
13:59
why?
soupless
soupless
Because I can choose zero elements from $B$ and let that be the element of $A$
which makes $A$ an empty set
Math
Math
use the logical def I provided and plug in the empty set for A is the statement true or false ?

« first day (3571 days earlier)      last day (1202 days later) »