I disagree. I too have a graduate degree in mathematics. I find it difficult to believe that all of the mathematicians decided at the same time that certain symbols would be used for certain words/phrases for the sake of "elegance". Like anything, the mathematics language has evolved over time. I agree that eventually the "elegance" of a proof became involved, but I equate the "elegance" with shorter proofs (it would get very annoying writing "which implies" about ten times in a proof). However, all I have to do is grab three or four graduate math texts of my shelf and start comparing theorems and proofs, and I easily find that the math language is still mixed with the English language, and not in a completely consistent manner. I don't know if mathematical historians have examine the notation development itself, but it would be interesting to know the historical perspective. BTW: Did you ever notice that for most word/phrases that have a symbol in mathematics have one or sometimes two symbols, except for " by contradiction"? Craig Eric Kaljumagi wrote: > > The funny thing is that this has happened before. In mathematics much > of the > > notation was basically to remove English words from the flow of a > proof or > > solution. Phrases such as "therefore", "there exists", "there exists > a unique", "is > > a subset of", "such that", "is an element of", "thus the theorem is > proved", "by > > contradiction" etc, all have been given single character symbols in > mathematics. Of > > course it took longer to develop than the IM shorthand. Fortunately I > never tried > > to use any of those symbols in my writing assignments. > > Although mathematics certainly has developed shortcuts (e.g.: '3 + 2 = > 5' for 'Three combined with two is five'), I don't think the intention > was to remove English words. Rather, the intention was to remove ALL > words, thus creating a 'language' that was portable throughout the known > world. > > As a graduate student in mathematics a decade ago, I wrote quite a few > proofs in English, and I'm quite certain that my professors would not > have allowed mathematical abbreviations in my writing outside of the > most basic (e.g.: '42' for 'forty-two'; 'n -1' for 'one less than > "n"'). The reason for my confidence is because I attempted to use math > notation in my writing back then, and I routinely failed to convince my > professors that such was appropriate. From what I can tell, > mathematical abbreviations are always to be used when working problems > but only used when writing about problems when the alternative would be > too inelegant. > > QED? > > Prof. Eric Kaljumagi > LAC/Math > Mt. San Antonio College > > To Unsubscribe, > send a message to [log in to unmask] > In body type: SIGNOFF LRNASST. To Unsubscribe, send a message to [log in to unmask] In body type: SIGNOFF LRNASST.