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I defined a notion (say, some kind of equivalence) in three forms, the first implies the second, which in turn implies the third.

I would like to use "strong", (nothing), and "weak" to describe them. But some one of great importance already used "weak" for something strongly related to the second form. To be compatible with previous studies, I have to refer to the first as "strong", to the second as "weak".

The third is weaker than the weak. I need an adjective to describe it. "Weaker" is not good enough. The notion also induce an adjective (e.g. equivalent) and a verb (e.g. equal), so I also need an adverb. "Weakerly" sounds strange.

Is there a standard adjective to describe the third notion? I now use "feeble".

I also see the possibility of defining a "stronger than strong" form. Suggestions are also welcome for this.

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    $\begingroup$ Why not change the name of the middle one to "moderate" and use "weak" for the weakest? Otherwise you could simply qualify it to "super weak" or something like that. $\endgroup$ – Gregory Grant May 24 '15 at 18:27
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    $\begingroup$ superweak, ultraweak $\endgroup$ – jkabrg May 24 '15 at 18:39
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    $\begingroup$ It would be epic to migrate this to English SE :-) $\endgroup$ – punctured dusk May 24 '15 at 19:16
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    $\begingroup$ are you sure you need to use the term weak? be a bit more creative! for example in probability one gets convergence almost surely => in probability => in law (also known as weak). You can take inspiration as how and why this new type of convergence was defined in the first place. Say you need it to show that a certain property, called "friendly" holds. Call this new type of convergence friendly convergence, or something like that! just an idea :) $\endgroup$ – Ant May 24 '15 at 22:29
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    $\begingroup$ "Totally weak." -- Eric Cartman. $\endgroup$ – David Richerby May 24 '15 at 23:22
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I don't think there is a standard adjective to describe this. If there is, we would need to know the context of the terms stronger and weaker to answer. It sounds like you are defining this weaker-er notion in your paper (since you have to introduce a new term), so it is really on you to give it a name. Now to compile a list of suggestions:

  • subweak
  • weakerer
  • superweak
  • ultraweak
  • extraweak
  • weak' (weak prime)
  • weak*
  • weak$^2$ (weak squared, or weak two, or too weak)
  • feeble
  • anemic
  • fragile
  • puny
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  • $\begingroup$ Great (and interesting) list, thanks. $\endgroup$ – Hao Chen May 24 '15 at 18:45
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    $\begingroup$ I like the tension between "subweak" and "superweak." Which is weaker? :P $\endgroup$ – Noah Schweber May 24 '15 at 19:14
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    $\begingroup$ More seriously: "ultraweak" is already used, in mathematics and biology/physics. $\endgroup$ – Noah Schweber May 24 '15 at 19:18
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    $\begingroup$ @Noah: Feeble is also used: a topological space is feebly compact if every locally finite open cover is finite. $\endgroup$ – Brian M. Scott May 24 '15 at 22:28
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    $\begingroup$ If the "weaker" one is a weakened version of the "weak" one, perhaps just go "weak weak", as in "the weak weak form", because it's the weak form of the weak form. $\endgroup$ – Glen O May 25 '15 at 16:10
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I can't resist adding this one to the list: what do you call a principle weaker than Weak Konig's Lemma?

Funny you should ask . . . (Weak Weak Konig's Lemma)

Ayup, we're a creative bunch. :P


Oh my goodness: page 18, after proposition 9.1. It's merely suggested, but: "Weak Weak Weak Konig's Lemma."


And heaven forbid we be at a loss to describe something not as weak as weak! (Page 8, definition 4.5.) "Strong weak truth table reducibility"

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    $\begingroup$ got me thinking weak$^2$ $\endgroup$ – jkabrg May 24 '15 at 19:08
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    $\begingroup$ Can you please bring the linked content into your post? Thanks $\endgroup$ – JustinJDavies May 25 '15 at 8:50
  • $\begingroup$ And in your first link, we find then that (Theorem 1.7) the DNR is striktly weaker than the WWKL. Where does this all lead us to... $\endgroup$ – Gottfried Helms Feb 1 at 12:28
  • $\begingroup$ @GottfriedHelms Well, that's different: DNR isn't a principal of the form "Every [property] binary tree has a path," so - although there's an obvious connection - it's not really of the type of this question. $\endgroup$ – Noah Schweber Feb 1 at 13:56
  • $\begingroup$ @Noah - ok, thanks for that information. I tended now to withdraw that comment, but maybe someone else might have the same idea - so better I leave it here? $\endgroup$ – Gottfried Helms Feb 1 at 14:11
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I would say "pathetic" or "puny".

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In PDE theory, the term "very weak solution" is in wide use. Google results.

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Very weak, according to xkcd:

enter image description here

But, more seriously, you can also put it the other way.

For example, in case of the Riemann Hypothesis, the Riemann Hypothesis is implied by the Generalized Riemann Hypothesis, which is in turn implied by the Grand Riemann Hypothesis.

But that maybe overkill.

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An interesting challenge! A couple of additional ones I didn't see in previous answers:

strong > weak > light (adverb 'lightly')

strong > weak > delicate (adverb 'delicately')

strong > weak > wimpy (adverb 'wimpily') - sounds less formal but has precedents in technical areas.

strong > weak > tentative (adverb 'tentatively') - likely less useful, has overtones of non-strength attributes (eg: hesitation).

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How about double weak and triple weak?

Advantages:

  • Clearer in rank than normal intensifiers (sub, very, super, extra, ultra). A triple weak is clearly weaker than a double weak, while it is not clear whether a super weak is weaker than a very weak or not. If we have a stronger version of a weak proposition, but weaker than the normal one, then we can just renumber the ranks and all are good.
  • More natural in language than weak² or weak*, and less redundant than weak weak
  • Reduce cognitive load for the naming, and leave more energy to actually studying it
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    $\begingroup$ To me comes into mind:"the mother of weakness" or so. Then more creative might be the addition of qualitative terms like "that proposition is lousy weak" or "absurdely weak" ... (not really serious, though...) $\endgroup$ – Gottfried Helms Feb 1 at 8:27
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    $\begingroup$ I just suggest using "double" or "triple" as a way to avoid confusions made from "very" or "super", as the question asks. Anyway, your proposition is hilariously strong. $\endgroup$ – Ooker Feb 1 at 10:39

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