While there are an infinite amount of numbers we have not named them all by unique names. And so far we have not named any number “bajillion” yet. And it would be confusing to use that name anyway as it can be easily confused with billion.
Edit: Since this reply /u/SrPeixinho have officially named 12980055490033 the bajillion and therefore ending the discussion once and for all.
Strictly speaking, no. Even assuming that all numbers must be named, you could construct it so that numbers past the named universe are simply multiples of prior numbers. For example, if we had nothing past “million,” we could say “thousands of millions” for billions, and “millions of millions” for trillions, etc. So strictly speaking no need to repeat, though at some point you’d be talking about a million million million million million atoms.
If we decide that we’ll get a new word of that sort every few orders of magnitude, it’s still not guaranteed that one is “bajillion”: yes, there are infinite numbers, but there are also infinite words that aren’t bajillion. Infinities are weird like that.
A child’s imagination and wonder should be encouraged. I for one, believe this kid is speaking the truth, as I will explain:
There is no hard/fast rule that says a number of English-speaking mathematicians have to agree with your choice of name for any nameless number out there. So yes, a child or anyone else, may name a number anything they like. Numbers are concepts, not real objects. So, imagining its name is good enough to make it true.
does that mean that there must also be a real number “pancake”?
just because there are infinite word sounds and infinite numbers does not mean that every word sound is paired with a number and vice versa; numbers don’t inherently have names the same way words don’t inherently have numbers.
the sound “bajillion” only corresponds to a number if people agree what a bajillion is.
There are infinitely many even numbers, but none of them are 3. Just having infinitely many of something, doesn’t mean that every “possibility” will “happen”.
The numbers have the names that we have chosen to give them. We could (and for all I know, already do) name a number bajillion, but our choice to do that has little to do with nothing to do with infinity.
While its true that there are infinite numbers, its also true that there is no limit to the number of letters that can be in a word.
If we had a number system that could go on naming forever, the names could just get longer and longer (and you would never see “bajillion”).
But just for fun, lets imagine that we decided that we don’t like really long words and want to put a cap on it. Say, no more than 100 letters.
In that case, you could confidently tell them that there would in fact, be a number called “bajillion” 🙂
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