I find it interesting to view a number comparatively as a counting number, a whole number, an integer, a real number, etc. etc. etc. I feel that going through this process can lead us to a further understanding of math, of engineering, of logic, etc. I will throw some questions out there for your possible consideration. As a weird side note, years ago I did a similar thread on Linkedin within an interest group. It drew quite a few comments. One day the thread was gone with no explanation. Only time that ever happened. I asked for an explanation and never got one. I started the thread as looking at the number "4". Only thing I could come up with is, that once when I was involved in selling some real estate, the real estate agent said there might be some reduced interest, because some people consider the number unlucky.

And just to be clear, we all understand the symbol "4" has clearly different meanings when considered as an integer, a complex number (4 + 0i) etc. In the same way the word "run" or the word "set" has clearly different meanings.

So, some questions:

Is there a natural progression to the way human cultures view numbers?

Does the way it is presented in math classes differ from the above, and is this interesting or informative?

Are there some numbers which are particularly inherently interesting?

Do mathematical operations and concepts develop in a natural order - counting, comparison as to quantity, estimation, negation, etc. etc. etc. ?

Some simple examples - when we say 1 million divided by one million is one/is equal to one, is that really the same as saying you have one penny?

When we say we add 4 and 1/3 and get 13/3, are we switching between meanings or is it simultaneously an integer and a real number?

When we say, 0.999999.... with a line over it is the same as one, isn't that by definition, changing meanings, going from one the counting number to one the limit of a process?

And just to be clear, we all understand the symbol "4" has clearly different meanings when considered as an integer, a complex number (4 + 0i) etc. In the same way the word "run" or the word "set" has clearly different meanings.

So, some questions:

Is there a natural progression to the way human cultures view numbers?

Does the way it is presented in math classes differ from the above, and is this interesting or informative?

Are there some numbers which are particularly inherently interesting?

Do mathematical operations and concepts develop in a natural order - counting, comparison as to quantity, estimation, negation, etc. etc. etc. ?

Some simple examples - when we say 1 million divided by one million is one/is equal to one, is that really the same as saying you have one penny?

When we say we add 4 and 1/3 and get 13/3, are we switching between meanings or is it simultaneously an integer and a real number?

When we say, 0.999999.... with a line over it is the same as one, isn't that by definition, changing meanings, going from one the counting number to one the limit of a process?

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