General Term Encompassing "Ascending" and "Descending"

Question

Is there a general term that encompasses "Ascending" and "Descending"? What I would like to say is that a number may be doing one of three things: ascending, descending or having an unknown . I want to avoid something like "vertical direction" since this is misleading. (For example, it may have a horizontal direction or no direction at all.)
Many thanks in advance for any help,
Peter.

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[nq:1]Is there a general term that encompasses "Ascending" and "Descending"? What I would like to say is that a number ... like "vertical direction" since this is misleading. (For example, it may have a horizontal direction or no direction at all.)[/nq]
Modulating?
It's difficult to say without knowing whether these numbers are describing a physical ascent (up and down a hill) or a figurative ascent (music, points on a graph).

David
==

Usenet · Answer

[nq:1]Is there a general term that encompasses "Ascending" and "Descending"? What I would like to say is that a number ... like "vertical direction" since this is misleading. (For example, it may have a horizontal direction or no direction at all.)[/nq]
Numbers don't ascend or descend, although a sequence or function may. The word you are looking for is probably monotonic or monotone. A sequence or function monotonically increasing in value is sometimes called an "isotone" (don't try to make sense of that isotone also means "order-preserving); one monotonically decreasing in value is sometimes called an "antitone".
If f(x) > f(y) for all x > y or
f(x) y
then f is strictly monotonic.
If f(x) >= f(y) for all x > y pr
f(x) y
then f is weakly monotonic.
If the domain of x over which f(x) is monotonic is the same as the domain of f(x), it is globally monotonic; otherwise it is possible (in fact normal) for a function to be locally monotonic over a subdomain.

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[nq:1]Is there a general term that encompasses "Ascending" and "Descending"? What I would like to say is that a number ... like "vertical direction" since this is misleading. (For example, it may have a horizontal direction or no direction at all.)[/nq]
Trend?

Odysseus

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[nq:1]Is there a general term that encompasses "Ascending" and "Descending"?[/nq]
Scending?
~Iain

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[nq:1]one of three things: ascending, descending or having an unknown .[/nq]
By "unknown" do you mean indeterminate, or do you mean momentarily static as at an extremum or an inflection point? If the latter, you might say it's "hovering."
¬R "I love Blip just because it's the absolute opposite of fun" http://users.bestweb.net/~notr/travelog/19990710.html Kibo

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[nq:1]Is there a general term that encompasses "Ascending" and "Descending"? =A0What I would like to say is that a number ... example, it may have a horizontal direction or no direction at all.) Many thanks in advance for any help, Peter.[/nq]
Changing altitude covers all three.
Alternatively they may be rising, falling or maintaining height.

They may even be floating, soaring or swooping..

Climbing, diving or even dropping like a stone...
There really is no shortage of options.
=2E..

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[nq:1]Is there a general term that encompasses "Ascending" and "Descending"? What I would like to say is that a number ... example, it may have a horizontal direction or no direction at all.) Many thanks in advance for any help, Peter.[/nq]
Moving?

General Term Encompassing "Ascending" and "Descending"

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