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

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1. Apr 17, 2015

### 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/Quick-Calcul...qid=1429297938&sr=8-1&keywords=quick+calculus

Last edited by a moderator: May 7, 2017
2. Apr 17, 2015

### Staff: Mentor

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.

Last edited by a moderator: May 7, 2017
3. Apr 17, 2015

### lonely_nucleus

I really appreciate you clearing that up for me friend.

4. Apr 17, 2015

### SteamKing

Staff Emeritus
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.

5. Apr 17, 2015

### Emmanuel_Euler

there must be (x)

6. Apr 17, 2015

### Staff: Mentor

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.

7. Apr 18, 2015

### 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.

8. Apr 18, 2015

### Emmanuel_Euler

you are right

9. Apr 18, 2015

### pasmith

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

10. Apr 18, 2015

### lonely_nucleus

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..

11. Apr 18, 2015

### pasmith

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.