# What's the word for the reversability of equal and opposite actions?

I'm trying to describe a desirable behaviour in user-interfaces (computer interfaces and machine interfaces) such that if you do the action and its opposite action once or more than once (assuming you don't reach an edge/limit) you should end up in the same state.

For example:

1. Pressing right moves the cursor right one character and pressing left moves the cursor left one character. If you press right five times then left five times the cursor will be in the same place, because right and left are `______`.

2. Undo and Redo are `______`. If you Undo 3 times then Redo 3 times you should be back to the same state.

3. Of a tool where the effect of one control depends on the current value of another control:

The length and radius controls are NOT `______` when used together. Length is `______` while radius remains fixed and radius is `______` while length remains fixed, but adjusting either breaks the `______ity` of the other one.

Answers to this question offer some good hints, but I don't think any of those are quite right. "Commutative" and "Associative" seem somehow appropriate, but are clearly specific to mathematics.

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Newton's 3rd Law :P – Josh Dec 17 '13 at 19:33
This doesn't answer your question, but the word's "discrete" and "quantized" come to mind, only because these actions must be so for the behavior you describe to take place. – Josh Dec 17 '13 at 19:34
@SoylentGreen I thought you were right at first and was editing 'discreet' in, but I realised that in the length/radius example, length may be implemented by a wheel rolling along a curve controlled by radius. Turning the wheels would be a "continuous" action, not a "discreet" one. – jhabbott Dec 17 '13 at 19:40
Please note I changed "discreet" to "discrete". Totally different meanings. I was thinking of "discrete" when I first penned the comment. I realized I misspelled it, so I made the edit. – Josh Dec 17 '13 at 19:59
how about counterparts? – user13267 Dec 18 '13 at 8:55

Right and left are inverses or complements (in the limited sense that they are "either of two parts or things needed to complete the whole; counterpart."). They are also counterparts.

But this is a little different from what you're asking for in the title.

• Associative is a property when it doesn't matter what order you press them in (e.g., LLRR is the same as RLLR). This is borrowed from the math concept (e.g., 3+2 is the same as 2+3).
• Invertible is a property when it has a counterpart (e.g., Ctrl-Z is invertible with Ctrl-Y, but Ctrl-C is not invertible).
• (Reversible is another way to say invertible.)

You might also consider borrowing terms from set theory (such as L and R form an identity), but that might be too much baggage for a straightforward notion.

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I went with actions and their counter-actions and discussed them as complementary to give context to the term and how I was using it. – jhabbott Dec 18 '13 at 2:57

I'd suggest "inverse" or "inverse functions"

adj. Inverted in position, order, or relations; that proceeds in the opposite or reverse direction or order; that begins where something else ends, and ends where the other begins.

Source: OED

For example, the inverse of left is right. Mathematically, the inverse of the derivative is the integral. Etc.

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I would like to suggest counteraction and adjustable.

counteraction noun
a force or influence that makes an opposing force ineffective or less effective

Here is how I would use them in your examples,

1. ... because right and left are counteractions.
2. Undo and Redo are counteractions.