Operator "Not equal to"

[scout51]

Just to get this concept straight...

The expresion !(x > 10), is equivalent to (x < 10) ?

or the expresion means that, if !(x >10) , can be (X <= 10) ?


Thanks in advance for your help.

[firedraco]

!(x>10) means x <= 10.

Draw a number line if it helps.

[scout51]

ok, so under the same concept.. the expresion !(x< 0) is true only if
(X >= 0) ?

[JLBorges]

If a and b are two integers:

( a>b ) implies ( b<a )

!(a>b ) implies both ( b>=a ) and ( a<=b )

( a>b ) || ( b>a ) implies ( b!=a )

!(a>b ) && !(b>a ) implies ( b==a )

Note: the relation > on the set of integers imposes a strict ordering.
http://mathworld.wolfram.com/StrictOrder.html

It is irreflexive: ( a>a ) is false for every a
Asymmetric: if ( a>b ) is true, then ( b>a ) must be false for every a, b
Transitive: if both ( a>b ) and ( b>c ) are true, then ( a>c ) must be true for every a, b, c

[scout51]

Thank you for your help guys, it really helped a lot.