I understood último means 'most recent' and final 'the very last'.
Now in my language course, I read:
El sábado es el último día de la semana.
How should I understand that?
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The word último indicates a position, it is an ordinal adjective, and therefore it precedes the noun.
For its part, final indicates a characteristic, it is a qualifying adjective and therefore follows the noun.
It is not normal to reverse your order, unless it is in poetic texts.
Me comí la última cucharada.
Me comí la cucharada última.
Me comí la cucharada final.
Me comí la final cucharada.
Apart from this grammatical difference, its meaning is the same.
The word último in its first meaning according to the dictionary is
Que está al final de una línea, de una serie o de una sucesión.
This means "something that is at the end of a line, series or sequence". For me the word último conveys an aspect of temporarity, this is, something can be último now but not necessarily after some time (though it could). A typical example is when you are going into a store and ask "¿quién es el último?" to inquire who was the last one to arrive.
On the other side, something final for me is something definitive. Think of a chess match, if you say "la última jugada" you mean "the last move of the match (so far)" (the last in a sequence, it can also be the final one or not), but if you say "la jugada final" you mean "the move that ended the match" (there can't be any more moves).
So if you say "el sábado es el último día de la semana" you are just saying that it is the last one in a sequence of days. In fact, if you say "el sábado es el día final de la semana" it sounds a bit weird to me though it's correct (it sounds to me as if there won't be any more days after that), it's just that we say "el último día" and we're used to that expression. Maybe a proper example could be "el sábado es el día final para aprovechar las rebajas", meaning that there won't be any more days after that to go to the sales.
Well, your question is a bit tricky because último and final can be synonymous.
According to the DRAE
- adj. Final, definitivo.
In our calendars, saturday is not the last day of the week, it's sunday. But if you use a calendar like this one, sábado is último and last as well. They are synonyms in this context. Último is a bit more idiomatic in your sentence but both are correct, taking into account that final should be positioned after día.
El sábado es el día final de la semana