User talk:Suprahili

I completely agree that this view is not intuitive if one is used to the proper definition, because then

dx

is just some syntactical delimiter capturing the variable

x

, not some kind of second variable. I recognize many people do find your view intutive, but I feel it's kind of like making up an interpretation of the symbols distinct from their actual definition. Thus there should at least be a link explaining this viewpoint (can this stuff be made rigorous with differentials?). Suprahili (talk) 22:14, 19 May 2009 (UTC)[reply]

dx is not just a syntactical delimeter. It does in fact bind a variable, but consider the situation where f(x) is in meters per second and x (and so also dx) is in seconds. Multiply them and get meters. That's not just syntactical delimiting. Moreover, the "proper definitions" were obviously not what Leibniz had in mind when he introduced this notation in the 17th century. The intuitive explanation given is in line with the way Leibniz did it. And it is useful. Was Leibniz "making up an interpretation distinct from the actual definition", when in fact the "actual definition" came two centuries later in the 1800s? Suprahili, have you ever heard that the world existed before the 21st century? Michael Hardy (talk) 00:49, 20 May 2009 (UTC)[reply]

No, in fact I think that the world is only 300 years old, but that's another story... ;->

I did not say there is no use for this intuitive interpretation, just that it seems to be an intuitive story woven to explain, almost like the mnemonic "My Very Educated Mother Just Served Us Nine Pizzas" for the planets. The current definition(s) do not give 'dx' more of a meaning than to bind variables, AFAIK. Hence my suggestion to include some link to an explanation for this viewpoint (you would think the integral page would have one). Suprahili (talk) 17:40, 20 May 2009 (UTC)[reply]

It's not like those arbitrary mnemonics. It makes sense to view dx as an infinitely small increment of x, and ƒ(x) dx as a corresponding infinitely small probability.

I certainly agree that the integral page should explain this standard idea. Michael Hardy (talk) 22:10, 28 May 2009 (UTC)[reply]