OP, you could try control-clicking and seeing if there is an "open-with" option to open your application with. Is this problem new, or has it been something that has only occurred in the last few days? Have you done anything (e.g. installed some new software, upgraded the OS to OSX Mavericks, etc.) that could possibly cause this issue? Do you have Virus Protection or a highly-restrictive firewall that limits your application usage (this has been known to happen, as Java is a particularly... vulnerable coding language)? We understand you have a problem, but knowing a little more detail will help us to pinpoint it and help you fix it.

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Disk image? To a Mac that's either a .dmg file or a .iso, to name the most common ones. Did you try re-downloading? Are you sure it wasn't renamed in the Application folder? This isn't a local home user issue, it's a system one.

I don't know how to check that.

I am the admin.

Are you the admin on the computer? That could be the reason why it won't let you run MC.

I cant download Java 7? Can only download latest version

I know, its because your on a mac! jk

*Back-up your worlds* Delete all of your minecraft files and try to launch the game again.

The new java made my minecraft stop. Install java 7. It should run fine!