On the Third Hand

Some uses for Classifications, Definitions, Refining definitions, and Re-purposing words. On the one hand: Why do we drive on a parkway, and park on a driveway? Shouldn't hot water heaters be called cold water heaters? If the water is already hot, why heat it? Shouldn't there be another word that sounds like the word homonym but means something different or is spelled differently? See #3. Homonym apparently isn't precise enough to distinguish all possible cases. Therefore, we refine the concept with homophones, homographs, heteronyms, heterophones, heterographs, capitonyms . . . I'm not making these word up* . Even though I have difficulty remembering the distinctions among these more precise categories , I understand that for linguists, the ability to distinguish among various types of homonyms could be useful. For example, a capitonym changes its meaning or pronunciation when capitalized. For example furniture polish is not pronounced like Polish

Part of a student's difficulty with simplifying expressions is the blurry extension of real number operations beyond the dyadic operators of add and multiply in the field properties. For conciseness, an "agreed-to" order of operations must then include non-field operators (dyadic and monadic) and semi-logical operators. The field properties do not specify that multiplication comes before addition, and most certainly does not demand that exponents be done before multiplication. Indeed, radicals, division, and subtraction operations are usually defined at the elementary level in terms of conversion to their inverse operation: radicals to exponents, division to multiplication, and subtraction to addition. Indeed, any algebraic expression with mixed operators requires punctuation in the form of grouping symbols to specify the priority of operations UNLESS the writer and reader agree to an order of operations for incompletely punctuated expressions. Even the simplest mixed