Gravitational Potential Difference in Uniform Gravity Field

[D H]

then according to the definition the potential difference between these points is infinity subtracted from infinity

Which is mathematical nonsense. You are not using the correct definition of potential, and you are being very stubborn about it. Stubbornness can be a useful trait at times, but not when it impedes your learning.

 

[Doc Al]

If the potential at a point according to the definition is infinite, and the potential at another point is infinite, then according to the definition the potential difference between these points is infinity subtracted from infinity

That should tell you that using "infinity" as a reference point is silly. All that physically matters is the change in potential between two points, which is well defined and trivially calculated. For a uniform field, choosing infinity as a reference is asinine.

You are hung up on a definition of gravitational potential that uses infinity as a reference, which is of limited use. Time to move on.