IS this quantified formulae true over the NATURAL NUMBERS (1,2,3,...)
for all x there exist a y for all z there exist a w [xy = w + z]

Question

IS this quantified formulae true over the NATURAL NUMBERS (1,2,3,...)
for all x there exist a y for all z there exist a w [xy = w + z]

ganeshie8 · Answer

consider

x=1, y=1

zarkon · Answer

why would we consider that?

anonymous · Answer

Ah ok because if x and y are both 1 their product will be equal to 1 and w+z  will always be greater than one since they can only be natural numbers (1,2,3,...) 
thank you

zarkon · Answer

it doesn't say for all x and all y ..it says for all x there exists a y

anonymous · Answer

hm... yeah you're right

zarkon · Answer

if you pick any x or z I can show there exists y and w such that the equation holds

zarkon · Answer

do it this way....pick any x and z

then choose y to be a number such that x*y>z

then choose w to be x*y-z

zarkon · Answer

then the equation holds