Question

What well-known set is this:\[\large\{n\in \mathcal N |(n>1)∧(\forall x,y\in \mathcal N)[(xy=n)⇒(x=1∨y=1)]\}\]

Answer 1

too large
\[\{n\in \mathcal N |(n>1)∧(\forall x,y\in \mathcal N)[(xy=n)⇒(x=1∨y=1)]\}\]

Answer 2

...

Answer 3

what are you trying to convey with that symbols?

Answer 4

im trying to simplify the set

Answer 5

how do you read that?

Answer 6

n belonging to natural number , n>1 and for all x,y belonging to natural number ,
xy=n gives , either x=1 or y=1
thats true ....u need to simplify this ?

Answer 7

it should be equal to a well know set , im still not sure which one

Answer 8

i think all the bit in the squar brackets is saying is
either x or y is n

Answer 9

These are THE PRIME NUMBERS - here is the (believe me) very readable reading of your definition:

Answer 10

I am reading - completely as an English sentence - so direct:
The set of all Naturals, such that if two other naturals x, y form a product equaling the considered member of our set, they

Answer 11

must satisfy either of the 2 options : either x = 1 or y =1

Answer 12

Which means, that either (x=1 and y = n) OR (x=n and y=1)

Answer 13

So in our human speech we say:" if there is a factor to n, this factor is either1 or n itself"

Answer 14

prime

Answer 15

That makes so much sense now !,
i totally get it

before i was trying to read it like
"The set of n where n is a natural number such that...."

and i didn't understand before how to apply the square braket bit

the way you put it
"The set of all Naturals, such that "
is much more elegant and clear
thankyou Mikael
\[\Large\textbf{BRILLIANT }\]

Answer 16

@Mikael awesome lucidity

Answer 17

http://www.amazon.com/Puzzles-Including-Mathematical-Features-Discovery/dp/0812921178

Answer 18

\[\color{red}{\text{PLEASE ! ALL PRESENT ! EVERY MAN WHO EVER} \\ {\text{ LIKED RIDDLES OR MATH MUST READ THIS BOOK !}\\ IT \quad IS\quad WIDELY\quad AVAILABLE}}\]

Answer 19

The book by Dr. Raymond Smullyan is agateway to mathematics and thinking to any kid ar grown up above 10-11 years and to 99 years

Answer 20

Lady or the Tiger? And Other Logic Puzzles Including a Mathematical Novel That Features Godel's Great Discovery