Using that bijection, you are still describing two sets of coordinates, you have just encoded them into a single number by interleaving them. Also, you won't be able to define points in certain quadrants of the cartesian coordinate space using that system because you have no way to make just the x coordinates or just the y coordinates negative. Depending on how you define the meaning of a negative interleaved coordinate, you could have access to any pair of two quadrants (+x/+y and -x/+y or +x/+y and +x/-y, etc.).
Unless you just use the first two digits as sign bits - if num would encode to (x,y) then instead you have 00num = (x,y), 01num = (x,-y), 10num = (-x,y), 11num = (-x, -y)
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Using that bijection, you are still describing two sets of coordinates, you have just encoded them into a single number by interleaving them. Also, you won't be able to define points in certain quadrants of the cartesian coordinate space using that system because you have no way to make just the x coordinates or just the y coordinates negative. Depending on how you define the meaning of a negative interleaved coordinate, you could have access to any pair of two quadrants (+x/+y and -x/+y or +x/+y and +x/-y, etc.).
Unless you just use the first two digits as sign bits - if num would encode to (x,y) then instead you have 00num = (x,y), 01num = (x,-y), 10num = (-x,y), 11num = (-x, -y)