doodle jump game type question

Is it okay to let a player infinitely increase in the y-axis as the player continues to jump?

Yes , there is no problem in going infinite in any direction.

Technically, NO! it is not okay as nothing can store/encapsulate/hold the value of the never ending number that is infinity. All data types have their Max and Min values. Take an float, which is 4 bytes, which is 32 bits, calculating the number of numbers it can store is 2^32.

However in most game circumstances, most of the time yes, but accuracy of position will deteriorate as you approach around 10000 or some really big number as the float can reach massive numbers with a trade off of accuracy, you will still be able to move but itll round to the closet the float can encode the value to but youll eventually hit an overflow execption where youre trying to get the float to store a larger value that it can hold.

id suggest a quick scene movement where once you pass a certain height you move the whole scene down and vice versa, but thats only if you encounter the jerkyness.