How were the symbols "1, 2, 3, ect" accepted as substitutes for numbers across many cultures as opposed to each region using their own, different symbols?

by Doctrine_of_the_Mean
scarlet_sage

More can be written, but you might be interested in the FAQ section "History of Mathematics" . The most appropriate discussion appears to be "What caused Arabic Numerals to be accepted world wide, but alphabets developed such a wide variety?" by /u/Jooseman (a number of replies). You can also see "When and how did Asian countries switch to the use of Arabic numerals?" by /u/t-o-k-u-m-e-i for a bit more detail on Japanese usage.

This is not to discourage discussion. More questions, data, and debate are welcome.