Why don't energy levels become infinite in an infinite well or harmonic oscillator?

[dyn]

Hi
I'm confused about something from quantum mechanics but it concerns infinity and limits.
For an infinite well the energy levels vary as n² and for an harmonic oscillator the energy levels vary as n with n taking integer values in both cases with no upper bound.
In both cases there are infinite levels but I have been told the energy does not become infinite in either case.Why does the energy not become infinite ?
Thanks

 

[BvU]

'Have been told' isn't a very strong reference ...
Energy levels can exceed any value, as you say: no upper bound. Anything to disallow that ?

Besides the given that the energy supply of the universe is probably finite, I see no limit for this theoretical case.

 

[mfb]

There is an infinite number of integers, but every integer is finite. Same thing.

 

[dyn]

let me re-phrase my question. If the energy varies as n² or n , does it ever become infinite ?

 

[mfb]

What is "it"?
Every energy level has a finite energy.