Having an huge Issue with such that notation

[woeful berry]

Hello, im having a problem with such that.

Theres the thing that Im not english native speaker, but even then do I not really even understand such that in my language.

So theres this explanation

[woeful berry]

And this

I always read, it like

I have a great sense of humor such that I could be a clown

But thats logically wrong, isnt it

[pallid tapir]

you understand the definition of relation ?

define relation for me once

I will try to point out the misconception

[woeful berry]

I have A x A, which does take every Element of Set A and puts it into a pair so if A = {1,2,3,4,5} A x A = {(1,1, 2,2, 1, 2....)}

[pallid tapir]

I mean such that just means applying condition nothing else don't overthink

R = { (x,y) such that x + y = 2 and x,y belongs to R}

Choose x and y such that their sum equals 2 that's how i would read this

[woeful berry]

so I narrow down what x,y will be. But then again I would rather read the stuff after the such that first

[pallid tapir]

nah just read from left to right it will seem more logical trust me

[woeful berry]

0.0

[pallid tapir]

you can try like one of these problems and maybe i can help if u get it wrong

[woeful berry]

so R = is an ordered pair which will have that x + y = 2 and R belongs to. How can I add pairs, and how do I know R

[pallid tapir]

that way maybe you will understand it better

[pallid tapir]

Sets are collection of elements.
Relation is also a set but collection of ordered pairs like (x,y) where the x is picked from 1st set and y from 2nd set that's it

so you can write R by picking elements from both sets which satisfy the given condition

[woeful berry]

(i) there will be ordered pairs in the set, and only the x and y are taken from A x A where the product of 3 * x - y is 0, so if x = 1 y must be y = 3

[pallid tapir]

yes you are on the right track

[woeful berry]

whats wrong

it feels off

[pallid tapir]

now this (1,3) is a ordered pair which will be a element of relation R

[pallid tapir]

No its correct relax

[woeful berry]

yeah x = 1 y = 3

(1,3)

[pallid tapir]

Simple example

[coarse summit]

You can read "such that" as "on the condition that"

[woeful berry]

A -> B?

[coarse summit]

Or "that satisfy the condition that"

[pallid tapir]

the 3rd line is read as from left to right:

Relation R defined from set A to set B = {(x,y) }where x + y = 5 , x is from set A and y from set B

[woeful berry]

anything without that?

for some odd reason I dont grasp the "such that" wording. Its so weird

[pallid tapir]

☹️☹️

[coarse summit]

No

"Such that" = "where it satisfies the condition"

[pallid tapir]

yeah

[woeful berry]

ok I can try that

[pallid tapir]

yeah you will get comfortable after some problems

[woeful berry]

this must satistfy : this condition

[pallid tapir]

yeah u can read it like that as well

[woeful berry]

so "it" is pre : and after : "the condition"

[pallid tapir]

yes

[woeful berry]

so then again

How do you evaluate 3 = 1 + 2

nvm

So would you say it narrows more down from left to right?

[woeful berry]

Also do you have an real life sentence example of how you would apply this

[woeful berry]

i mean this

[coarse summit]

You can read ${y:y$ is even$}$ as "the set of all $y$ that satisfy the condition that $y$ is even" or "the set of all $y$ where $y$ is even"

[wary basin]

SWR

[woeful berry]

I mean like apples and so

Like theres an apple in the tree

[coarse summit]

What?

[woeful berry]

Such that

couldnt even abstract what I woulf say there

[pallid tapir]

these examples satisfy you ?

[woeful berry]

I mean totally without math

[pallid tapir]

The rules were designed such that no one could cheat.

what do you think ?

[woeful berry]

Yeah this is how I always understood this

But in mathmatical context its all weird

nope reading math again makes boom

[pallid tapir]

lol

you will get used to it

[woeful berry]

If been trying this for over 40hrs in 2 years

Just this one concept .

So much pain

Such that im willing to rewrite math

[pallid tapir]

its fine keep trying one day you may understand it randomly while you are in the toilet lol

[blissful zinc]

remember a set is a collection of objects, not just one object. if you want to make an abstract set, start with a larger group of things, then apply a condition or rule to them

for ${ y \mid y \text{ is even}},$ the larger set is all possible numbers, and the condition is that the numbers are even

[wary basin]

حسیب ♥

[woeful berry]

So its narrorowing down

[crisp parcel]

ramadan mobarak (sorry went entirely off topic)

[blissful zinc]

and we are using y to represent a number within this larger set

so (all integers) with the condition (is even) becomes $${ y \text{ is an integer} \mid y \text{ is even} }$$

[wary basin]

حسیب ♥

[woeful berry]

This is how I used to read it

[blissful zinc]

then that seems like a fine way to read it, as long as you're getting the correct information from the set

(which you seem to be)