Thanks to all of you for your replies. Once again, it seems that there are different responses to my question about NOT using a battery. As I said, I ordered a replacement battery and yes, it was only $17. However, as to the concept that an Apple battery would be better, the battery I removed today is an Apple replacement battery and it puffed up so much that it nearly exploded. In fact, the expansion of it was affecting the touch pad directly above it to the point of causing all sorts of problems in making it work AT ALL. Trying to go to websites by hitting the button below the keypad led to all sorts of very strange events, none of which was the one I intended for it to do. As such, I'm not a big fan of the Apple battery as it essentially failed miserably as far as I am concerned. In addition, I don't use the old MacBook for anything other than Spotify or Netflix connections in my studio while I work. My MacBook Pro is currently in the repair shop and I brought in the MacBook as a simple backup computer for e-mail and such, not for serious work on photography or other instructional things.
I went to Amazon to buy the battery. They were nearly ALL around that price. Even the Apple branded one was around $45 or so. Perhaps it's an outdated battery and they don't command such a high price anymore because no one is using them any longer. Again, this a temporary stopgap measure and all I really wanted to know was if it was safe to use the computer without the battery. Perhaps I'll just take Mac holiday until I get my MB Pro back fully repaired.
pjcaver