# When dependance exists between two quantities?

Suppose we have two quanitities X and Y and we try to find out if a third quantity Z depends on them.

1st case Changing the X holding Y constant doesn't change Z.

2nd case Changing the Y holding X constant changes Z.

3nd case Changing both X and Y (simultaneously) changes Z.

Can from the first two cases conclude that Z does not depend on X? What if we change both X and Y simultaneously and now Z changes differently than the 2nd change? For example if Y were doubled in the 2nd case then Z doubled but in the 3rd case doubling Y quadrupled Z (no matter what change X undergoes). Could we say in that case that Z does not depend on X?

• It is not clear if X and Y are independent variables or if they are the only variables Z depends on. This question is more suitable for Math SE or Cross Validated. – Conifold Apr 22 '20 at 17:38
• @Conifold Thanks for the answer. Can I transfer the question in Math SE or Cross Validated? – ado sar Apr 23 '20 at 17:55
• It will be faster if you delete it here and post there. – Conifold Apr 24 '20 at 13:39