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If you were not under any sort of employment contract, then it is true that your employer can terminate you at any time, for any reason, and without notice. The only exceptions here are if you feel you have been discriminated against because you are a member of a protected class, or if the reason for your termination was against public policy, or if you were terminated because you reported some sort of illegal behavior on the part of your employer.
If you DID have an employment contract, you could still be terminated, but your employer would have had to have justifiable cause.
On another note, because you were let go, you should be eligible for UE benefits in the event that you have trouble finding another job.
Unfortunately, no. The protected classes under Title IV of the Civil Rights Act are race, religion, gender, color, and national origin. Age is also considered a protected class. And yes, discrimination is very difficult to prove.