How to imply ‘1-ness’ properly?

Question

My question is about the words einzig ‘only, unique’, ein ‘a, one’, einzeln ‘single’, allein ‘alone, only’, ledig ‘single’ and einig ‘united’.

I’m always confused to use the words in a context. Do they have completely different usage or are they interchangeable from a specific point? And are there some other words that imply ‘a, single, one, unique’, except the ones I listed?

If these words refer to ‘one’, why do they have different usages?

Answer 1

There are differences:

• einzige = there is only one
• eine = one (but not the only one — sometimes used as “any”)
• einzelne = individual ones (can you hand over the nails to me one by one?)
• allein = alone, sometimes in the sense of ‘only’
• ledig = single, unmarried

Answer 2

The same goes for english, really! Let's try and translate some english words which imply one-ness into german and shower you with examples, to supplement Craig's answer.

one

• eins (number one -> Nummer eins)
• einer/eine/eines (one of them -> einer von ihnen)
• ein (one house -> ein Haus)

a

• ein (a house -> ein Haus)

single

• einzig (not a single word -> kein einziges Wort)
• ledig (relationship status)

sole

• einzig (the sole purpose -> der einzige Grund)
• einzeln, einzig (one sole tree -> ein einzelner Baum)
• ledig (negative connotations; one sole tree was left -> ein lediger Baum blieb übrig) - that might be a regional thing though (Lower Austria), I've never heard a german say that
• alleinig (the sole ruler -> der alleinige Herrscher)

solely

• lediglich (much more common than "ledig")
• ausschließlich (this message is directed solely towards you -> Diese Nachricht ist ausschließlich für dich bestimmt)
• einzig
• nur

alone (lone, lonely)

• einsam (lone wolf -> einsamer Wolf, "Einzelgänger"; I was lonely -> ich war einsam)
• allein(ig) (lone parent -> Alleinerzieher; I was alone -> ich war allein)

any

• irgendein (Give me any -> Gib mir irgendeines)
• kein (I don't watch any sports -> Ich schaue keinen Sport)

anything

• irgendetwas (Give me anything -> Gib mir irgendetwas)
• alles (I love you more than anything -> Ich liebe dich mehr als alles andere)

mere

• bloß (a mere shadow of his former self -> ein bloßer Schatten seiner selbst)
• schier (mere greed -> schiere Gier)
• nur

only

• einzig
• nur (only for you -> nur für dich)
• bloß (it was only a one-night-stand -> es war bloß ein One-night-stand)

Answer 3

Some further words of that group:

• einig - united in thought (thinking alike, in agreement). Darüber sind wir uns einig.
• einigen - come to an agreement
• geeint - united
• vereinen - to unite, from that vereint, Vereinte Nationen(UN) or Nach langer Trennung waren sie wieder vereint.(got back together). can be a euphemism for sex
• vereinigen - to unify/unite, from that vereinigt. This implies a strong union. Vereinigte Staaten(USA), Wiedervereinigung(Reunification), can be a euphemism for sex
• einzigartig - unique, often exchangeable with einzig. However, einzigartig is more an extremely special, while einzig means that there really is just/only this one object, person or opportunity. Compare a unique opportunity(eine einzigartige Gelegenheite) to the only opportunity(die einzige Gelegenheit)
• allein, einsam - alone, lonely. allein can mein only in some cases (as alone in English)
• einzeln - indivually (from a group) or a single one. Taking nails one at a time from a heap = Die Nägel einzeln von einem Haufen nehmen. Ein einzelner Nagel steckt in der Wand. Rarely applicable to persons (Ein einzelner Mann stellte sich der Meute entgegen. or Ein Mann stellte sich der Meute allein entgegen. But not Ich bin einzeln. That would need einsam or allein (or ledig if not lonely, but merely unmarried.)

They really have slightly differing meaning, regarding which kind or degree of one-ness or uniqueness is expressed. In most cases, their English cognates are restricted in a similar manner, however.

ein of course also is the indefinite article a/an in many cases, an no special one-ness is implied.