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Yeah; students often conflate numerals with numbers and assume that if two numerals are distinct then the numbers they represent must also be distinct. It's not
by dwohnitmok 1y ago
Yeah; students often conflate numerals with numbers and assume that if two numerals are distinct then the numbers they represent must also be distinct. It's not trivially true! You need to prove that distinct numerals lead to distinct numbers and as 0.999... vs 1.000... demonstrates it is not always true for various kinds of numerals and numbers!
I think teasing apart numerals and numbers is a good first step on one's journey in mathematical logic.
- mcphage 1y agoThere's also another numeral system called "Bijective Numeration" (https://en.wikipedia.org/wiki/Bijective_numeration https://en.wikipedia.org/wiki/Bijective_numeration) which does is a bijection between numeral sequences and numbers (hence the name). It's pretty neat... it doesn't have a 0, so you can't get an infinite string of trailing 0s.