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I'm not a math student. I can understand general basic math.

While solving many problems we take relations "a directly proportional to b" for granted and don't care to ponder what if it doesn't always hold all the way. Let me try to explain it a bit what I'm trying. If 'a' is proportional to 'b' for some known range, then does it mean it would always hold? I think gravitational force on some object is proportional to the distance from earth. But once the object has landed on earth, then this relation won't hold. Gravitational force is inversely proportional to the distance when being calculated from the surface of earth toward the center.

Is there any difference in saying "a directly proportional to b" or "a proportional to b"?

Please help me with this. Thank you for guidance and time.