„Byrja“ og „hefja“ eru samheiti, en „heitur“ og „kaldur“ eru andheiti.

Because the sentence is talking about the words themselves, not using them normally in a sentence.

So byrja, hefja, heitur, and kaldur are being mentioned as vocabulary items. Icelandic often marks that with quotation marks, just like English can do.

Also, Icelandic commonly uses „ … “ rather than English-style " ... ".

Because they are being given as dictionary-style verb forms.

In Icelandic, the basic form of a verb is usually the bare infinitive, such as byrja or hefja. The word að is the infinitive marker, and it is used when the verb is part of a clause, for example:

• Mig langar að byrja. = I want to begin.

But when you are simply naming the verb as a word, you normally use byrja, not að byrja.

Yes. They are the infinitive forms of the verbs.

That is the normal citation form for Icelandic verbs, similar to how English dictionaries list begin rather than begins or began.

Because Icelandic adjectives are usually cited in the masculine singular nominative form.

So the basic dictionary forms are:

• heitur = hot
• kaldur = cold

Even though the sentence is talking about the words themselves, Icelandic still uses the standard headword form for adjectives. It does not switch to a neuter form just because the words are being discussed abstractly.

Because heitt and kalt are not the citation forms; they are other inflected forms of the adjectives.

For example:

• heitur = masculine singular nominative
• heit = feminine singular nominative
• heitt = neuter singular nominative

And similarly:

• kaldur
• köld
• kalt

When Icelandic names an adjective as a vocabulary item, it normally uses heitur and kaldur, not heitt and kalt.

Because eru is the present plural form of vera = to be.

Each subject contains two items joined by og:

• byrja og hefja
• heitur og kaldur

Since the subject is plural, the verb is plural too:

• eru = are

• og means and
• en means but

So og links the two words inside each pair, while en introduces a contrast between the first statement and the second one.

Here they are understood as plural: synonyms and antonyms.

The important thing is that these words can look the same in singular and plural, so you often have to tell from context. In this sentence, the plural meaning is clear because:

• there are two words in each pair
• the verb is plural: eru

So samheiti here means synonyms, and andheiti means antonyms.

They are in the nominative.

After vera = to be, Icelandic normally uses a nominative predicate noun or adjective. Here the sentence is identifying the subjects as belonging to a category:

• Byrja og hefja eru samheiti
• Heitur og kaldur eru andheiti

So nominative is the expected case.

Not always.

They overlap enough to be called samheiti, but in real usage there can be differences in style and context. Very roughly:

• byrja is a very common everyday word
• hefja can sound a bit more formal or literary in some contexts

So the sentence is correct as a vocabulary statement, but in actual speech and writing, one word may sound more natural than the other depending on the situation.

Yes. A comma before en is very normal when it connects two contrasting clauses.

Here the sentence has two parallel parts:

• Byrja og hefja eru samheiti
• heitur og kaldur eru andheiti

The comma helps separate those two clauses clearly.