I"ve currently asked this a part of another question, yet thought it"d be easier to sophisticated a bit an ext on mine concern.

You are watching: Difference between ++x and x++

Let \$x\$ it is in a set. What is the difference in between \$x\$ and also \$x\$? I get that the latter is a collection consisting of a single element - namely \$x\$, however what is the difference?

For example, we deserve to have \$x\$ to be the set \$1\$, climate \$x=\1\\$. Aren"t those \$2\$ expression the same?

Another problem are the base - when we have actually a set, execute we always have to surround him with brackets, for instance, deserve to we have actually \$x\$ to be the collection \$2\$?

Thanks a lot

elementary-set-theory notation
share
cite
follow
edited january 26 "18 in ~ 8:20

Asaf Karagila♦
asked january 25 "18 at 13:32

asdfasdf
\$endgroup\$
9

31
\$egingroup\$
Think that the brackets as a bag you placed things in. Climate \$1\$ is a bag include the number \$1\$. Yet \$\1\\$ is a bag containing a bag containing the number \$1\$. So two bags, one inside the other. These room different. Physically various if friend think real paper bags.

re-superstructure
point out
follow
answered jan 25 "18 in ~ 13:38

Ethan BolkerEthan Bolker
\$endgroup\$
4
4
\$egingroup\$
\$\$1 \$\$ is a collection whose the unique aspect is the creature \$1\$

\$\$\1\ \$\$ is a set whose the unique aspect is the set \$1 \$.

share
point out
follow
answered jan 25 "18 at 13:35

hamam_Abdallahhamam_Abdallah
\$endgroup\$
7
| present 2 much more comments
2
\$egingroup\$
You room probably gaining confused between the surname of a set and that is description.When we compose \$A=x\$, we average \$A\$ is a set and inside collection \$A\$, we have an aspect \$x\$.

Now if I define another set \$B=A\$, then \$B\$ is a set and inside collection \$B\$, we have actually an element \$A\$, i beg your pardon is additionally a set. In this case, \$B\$ is a set of sets.

If you want to refer to the last set, writeits surname \$B\$, orits summary \$A\$.

For your last question, YES, we surround the aspects of the collection by curly braces , which also ensures unorderdness and also non-repeatability.

re-superstructure
point out
monitor
edited jan 25 "18 in ~ 19:39
answered jan 25 "18 in ~ 13:45

spkakkarspkakkar
\$endgroup\$
3
2
\$egingroup\$
Well if you have actually \$x=varnothing\$, then \$0=#x eq #x=1\$. So plainly both sets room not the same.

Edit: with \$#S\$ I describe the cardinality of a collection \$S\$, i.e. In the finite instance the number of elements in \$S\$.

re-superstructure
mention
follow
edited january 27 "18 in ~ 8:24
answered jan 25 "18 at 13:37
asdqasdq
\$endgroup\$
6
| show 1 more comment
1
\$egingroup\$
There is a practical distinction when friend think about how you can use these sets - namely together a domain that functions. A role that bring away a number is no the same as a duty that bring away a set.

re-superstructure
mention
follow
answered jan 25 "18 in ~ 14:42
Kevin OlreeKevin Olree
2355 bronze title
\$endgroup\$
1
\$egingroup\$
Perhaps it would be beneficial to imagine the distinction in concrete terms - speak in regards to a computer data structure. Expect we represent sets using connected lists . Then \$x\$ is (the head reminder of) a succession of nodes, where each node has actually a guideline to an element of \$x\$ and a pointer to the next node in the sequence. Climate \$x\$ is (the head tip of) a solitary node, whose element pointer points to (the head node of) the sequence of nodes representing \$x\$. Clearer?

share
mention
follow
answered january 25 "18 at 15:17
PMarPMar
1111 bronze argorial
\$endgroup\$

Thanks because that contributing an answer to stillproud.org Stack Exchange!

But avoid

Asking because that help, clarification, or responding to various other answers.Making statements based on opinion; ago them up with recommendations or an individual experience.

Use stillproud.orgJax to format equations. stillproud.orgJax reference.

To discover more, check out our tips on writing an excellent answers.

See more: ' Chicago P.D. Season 4 Episode 19, Last Minute Resistance

Draft saved

send

### Post together a guest

name
email Required, yet never shown

### Post as a guest

surname
email

Required, however never shown

## Not the answer you're feather for? Browse various other questions tagged elementary-set-theory notation or asking your own question.

Upcoming events
Featured ~ above Meta
5
the difference in between \$emptyset\$ and \$\emptyset\$?
1
Are the aspects \$c\$ and \$c\$ the exact same in a set?
3
How can it be the the empty collection is a subset that every set but no an aspect of every set?
2
Does \$\ = \\ cup \\ cup cdots cup \\\$
-4
Why is A intersection A' null?
0
Why is an aspect that belongs to a set that belongs to another set not an element of the 2nd set?
0
is or Ø an north set?
0
Set concept with north sets confuses me. Why is Ø ⊂ Ø false and also why is Ø ⊂ Ø, Ø true?
connected
10
Difference between a form and a set
1
Notation and also Quantifiers
4
Discrete stillproud.orgematics - set theory - Symmetric difference: Proof for a offered number.
1
sensible difference between d(total) and partial
19
Set, n-Tuple, Vector and Matrix — links and also differences
1
What is a wise means to intuitively describe to a layman the ide of identifying a collection with another?
2
Cardinality that the set of all stillproud.orgematical declaration
1
The official difference between \$cup\$ and \$vee\$
0
Is it feasible for a collection to contain non-stillproud.orgematical objects?
warm Network questions an ext hot inquiries

question feed