Music of the Primes..........interesting title.................what is one aspect of music..............???  Well several.......at once.........................same and different.............the chorus...........repeats................and the other lyrics of the song are different..............symmetry..........and asymmetry at once..................

If u overlapped the pf...........with the neg. integers.........starting at -1...........and working backwards...........repeating the pf................for every 10 neg #'s.........matching them up like that.........................u would get................10 (1's).................10 (-9's)..............10 (-19's), etc..................




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5 primes............5 non primes................the #'s 2 - 11...................as in..............2, 3, 4, 5, 6, 7, 8, 9, 10, 11................................overlap that with 1, 2, 3, 4...............................I get 3, 5, 7, 9, 11, 13, etc................the same exact sequence as taking difference of squares...............for positive numbers anyways..............

Whole Numbers

Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, ... (and so on)

No Fractions!

Examples: 0, 7, 212 and 1023 are all whole numbers

(But numbers like ½, 1.1 and 3.5 are not whole numbers.)

Counting Numbers

Counting Numbers are Whole Numbers, but without the zero. Because you can't "count" zero.
So they are 1, 2, 3, 4, 5, ... (and so on).

Natural Numbers

"Natural Numbers" can mean either "Counting Numbers" {1, 2, 3, ...}, or "Whole Numbers" {0, 1, 2, 3, ...}, depending on the subject.

Integers

Integers are like whole numbers, but they also include negative numbers ... but still no fractions allowed!

So, integers can be negative {-1, -2,-3, -4, -5, ... }, positive {1, 2, 3, 4, 5, ... }, or zero {0}
We can put that all together like this:

Integers = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }