Quick Calculus book uses Δ by itself, ex: (ln(x+Δ)-lnx)/Δ

[lonely_nucleus]

On the section on differentiation of logarithms and exponentials the book shows equations like this
(ln(x+Δ)-lnx)/Δ and it gives values for Δ, I do not understand why there is no variable following the Δ.

if you want to see the exact question I am trying to explain please look at page number 119 in this online version of the book: https://www.amazon.com/dp/0471827223/?tag=pfamazon01-20

 

[Mark44]

On the section on differentiation of logarithms and exponentials the book shows equations like this
(ln(x+Δ)-lnx)/Δ and it gives values for Δ, I do not understand why there is no variable following the Δ.

I'm not able to view page 119 from the link below. As to the notation, I believe the author is using Δ as a shorthand notation for Δx. That's a bit sloppy IMO.

if you want to see the exact question I am trying to explain please look at page number 119 in this online version of the book: https://www.amazon.com/dp/0471827223/?tag=pfamazon01-20

 

[lonely_nucleus]

I'm not able to view page 119 from the link below. As to the notation, I believe the author is using Δ as a shorthand notation for Δx. That's a bit sloppy IMO.

I really appreciate you clearing that up for me friend.

 

[SteamKing]

Well, the title of the book was Quick Calculus. It was apparently so quick that Δx became just Δ. Or there was a disagreement with the typesetter, who got back a little on his own.

 

[Emmanuel_Euler]

there must be (x)

 

[Mark44]

there must be (x)

It would be better if the author used Δx, but if he explains somewhere that he is using a shortcut, then no harm done, IMO.

 

[Gullik]

The author can use whatever symbol s/he wants? I've seen x +Δx, x + Δ, x+h. A book should usually be consistent in that it uses the same notation, but be used to several different notations for the same thing. Different notations usually have upsides depending on what is being discussed.

 

[Emmanuel_Euler]

It would be better if the author used Δx, but if he explains somewhere that he is using a shortcut, then no harm done, IMO.

you are right

 

[pasmith]

As to the notation, I believe the author is using Δ as a shorthand notation for Δx. That's a bit sloppy IMO.

\Delta is a perfectly good variable name, although h is more usual in that context.

 

[lonely_nucleus]

\Delta is a perfectly good variable name, although h is more usual in that context.

I do not like Δ being used as a variable name because it is an operator and it caused me confusion, I will have to deal with it but using Δ by itself is similar to using + by itself. Thank you for the reply, it gave me a good heads up..

 

[pasmith]

I do not like Δ being used as a variable name because it is an operator

Not inherently so, in the way that +, -, \times, \circ, \wedge ... are operators.

All letters are available for use as names of sets, objects and functions (a category which includes operators), and may be reused for different purposes depending on context.