If the non-compete clause is limited to what you have provided here, accepting employment with a competitor is not the same as setting up business as a direct competitor, and is therefore not a breach of the contract/agreement.
If, however, there is more to the non-compete than what you have quote here, you may want to review your circumstances with an attorney in your area. Enforceability if non-compete agreements is specific to the jurisdiction or state in which you are located, and is dictated by statute and by case-law.
I have personally seen non-compete agreements drafted by corporate attorneys in foriegn jurisdictions that can simply be disregarded, as they are wholly unenforceable under current WI case-law -
- the point is, just because there is a non-compete, don't assume that you are stuck with it!
I would need to see the non-compete agreement since the precise langauge will be key in assessing your situation. As a general rule however, non-competes are strictly enforced and any ambiguity will be interpreted against the drafter. In addition, they will only be upheld in Arizona if reasonable as to time (duration) and geographical scope.
The clause you described does not prohibit working for a competitor, but from starting a competitive business. However, if drafted properly, a non-compete might prohibit a person from working for a competitor after employment terminates. You should consult with an attorney to determine your rights and obligations in this matter.