Let A ={∅, {H,T}} and C = {}. Is C ∉ A or C ⊂ A or neither

[thin pulsar]

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[jade wyvern]

well look at both, is the empty set an element of A?

[ornate haven]

yeah so it cant be neither!

so I think ∅ and {} is basically equivalent

[jade wyvern]

yes they are

[ornate haven]

but don't know if set C is a element of set A or a subset

[jade wyvern]

both are symbols that denote the empty set

well is the empty set an element of A?

[ornate haven]

yea

[jade wyvern]

is the empty set a subset of A?

[ornate haven]

i think so?

[jade wyvern]

yes, {} C X for any set X

so $C\in A$ and $C\subseteq A$

[carmine scroll]

Omegabet_

[ornate haven]

so its both a element and a subset?

[jade wyvern]

yes

[ornate haven]

thats interesting the problem posed it as a either/or question

[jade wyvern]

ok

well it's yes, C is either not in A or is a subset

[ornate haven]

oh so its C ⊂ A

[jade wyvern]

yes

[ornate haven]

can a set be a element of another set?

[jade wyvern]

yes

you just cant have a set inside itself, or something akin to that (I dont remember the exact idea)

[ornate haven]

i think thats russell's paradox

dont remenber

[jade wyvern]

yeah, something like that

village barber paradox, whatever, tangent aside

[ornate haven]

+close