0,1,2,3,4,5,6,7,8,9

Did you know that in the standard mathematics base of ten there is a mnemonic for the often asked question (among other queries by students - American students I must add - whose previous education  left them quite defunct in rudimentary arithmetic skills which was the main cause of their difficulty in Algebra) in elementary algebra of 'what is 7*8 equal to?' -   I would point out that in the listing of the base numerals 0 through 9  you could quickly find 5,6,7,8 which would remind then that 56 = 7*8 .  and that also  1,2,3,4 would remind them that 12 = 3*4.

Aside from being a quick and easy crutch for them, it also led into a more interesting (even if minor) thought of did they think that such a scheme could be found in the base numerals of other bases - such as 8 or 12, or 36 or what ever.  A few of the interested students would usually assume that in a field of infinite base sets that there had to be more such random multiplication equalities.

However a little proof I had devised had surprised my by showing that only base ten held such base numerals.  Since those school teaching days are far behind me I have never thought much about this but I have never heard of this idea elsewhere.  If any of you gentle readers happen to be interested in number ideas and have cause to look into such a simple example I would be more than happy to hear your comment on the same