Question

is the empty set really a set? prove...

Answer 1

An empty set is a weird concept. Imagine we had a set, called A and it had no elements.

Since the items in that set (nothing) are still in that set, then it is a subset of A. Easy way to think about is that since we cannot find any element in subset A, then all the elements in the empty subset is in Subset A.

Answer 2

I don't know a mathematical way of proving it. maybe @iambatman knows how

Answer 3

Or @arabpride

Answer 4

Good question. Not positive, but I believe the name fits the concept quite well, because, although it may not contain any elements, it is still considered a set. I really don't think that answered your question but... I tired cx

Answer 5

see it like this , a set is like a box
if the box is empty or not it will still a box right /?
same with set it doesnt matter if its empty or non
its a set like a box

Answer 6

There is no mathematical equation as such to prove it. It is a mixture of common and mathematical knowledge

Answer 7

\[\large \phi = \{\}\]

Answer 8

^^ That is the symbol of an empty set, rather than typing {}

Answer 9

\[\large \phi = \{\} \approx \square \]

Answer 10

yeah somewhat close to a box :P

Answer 11

lol. It is a box if you have my drawing skills ;)

Answer 12

ganesh copy cut :P
\(\large \emptyset\)

Answer 13

whats the actual correct symbol for empty set ? \(\large \phi, \Phi, 0, \emptyset\)

Answer 14

\[\emptyset \]

Answer 15

even says empty set xD

Answer 16

The most accepted one is either the second or last symbol, but I am sure the others will be acceptable also.

Answer 17

Oh yeah `\emptyset` says it all :)

Answer 18

also there is another one mmm