There won’t be a “real” number bajillion until we decide to define the term in relation to a particular number. Right now it’s defined as “an indeterminate but exceedingly large number”.
Before someone decided to define a googol as a googol (Google it if you don’t know :P), there was no real number “googol”. Same for googolplex. Not that those numbers didn’t exist, but they hadn’t been defined in those terms yet. Maybe someday “bajillion” will have a defined number associated with it, but currently it doesn’t.
Edit: spelling
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