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In the first episode, when Kirito was showing Klein the ropes of combat, the
conversation goes

> Kirito: However, there is no magic.
>
> Klein: An RPG without magic? That is a bold decision.

However later on in the show, Kirito visits Lizbeth's shop in _Temperature of
the Heart._. Kirito is in shop for another sword, and shows Lizbeth his
_Elucidator_.

Lizbeth responds with:

> An Elucidator! This is the gnarliest **magic** sword a person can get from a
> monster drop.

If magic did not exist, how would there be a magic sword?


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sword-art-online
Was there truly no magic in Sword Art Online?


There is indeed no magic in Sword Art Online.

In your question, you're misunderstanding something important. Lizbeth doesn't
say that. She says that, "out of all monsters drops, this sword is good enough
to be considered in a maken (魔剣 cursed sword) class." which is like saying the
sword is in a class of its own. She doesn't say anything about magic.


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You misunderstood the context of Klein and Kirito's conversation. The line
directly preceding what you quoted is very illuminating.

> Kirito: I've heard there are an unlimited number of skills. However, there
> is no magic.  
>  Klein: An RPG without magic? That's a pretty bold decision.  
>  Kirito: Isn't it more fun to move your body as you fight?

Since the conversation is about sword skills, Kirito is undoubtedly referring
to magic spells, such as those that can be cast in Alfheim Online for such
effects as healing and illusion. He doesn't mean that no magic exists in the
world of Sword Art Online, just that there are no magic spells that players
can use. As such, the existence of a sword classified as "magic" does not
break this rule. Though since it has been noted that the magic sword may have
just been translated wrong, I'll note a few other magic things in Sword Art
Online: The floating castle, certain monsters, Silica's dragon, and the
revival item may all be classified as magic.


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In SAO, there are no magical spells that players can cast. However, according
to the light novel, SAO does have some magical items and aspects. Some of
these items include gems which players could use to instantly teleport, heal
or recover from poison. There is also the [Divine Stone of Returning
Soul](http://swordartonline.wikia.com/wiki/Divine_Stone_of_Returning_Soul)
that revives a fallen player.

[![Picture from the
anime](https://i.stack.imgur.com/pinRG.jpg)](https://i.stack.imgur.com/pinRG.jpg)

This text and the following quotes are taken from the second volume of the
light novel.

> The few magic items in this world where had been excluded were all shaped
> like gems. Blue was for instant teleportation, pink for recovering HP, green
> for antidotes, and so on. They were all convenient items that produced
> instant effects, but they were also expensive. So in most cases people used
> cheaper items such as slow-acting potions after running away from a fight

Certain parts of the game could also be considered magical such as the
teleportation gates used to move between floors, and the alters found in
churches. These altars would allow a player to bless their weapons when facing
undead opponents. Also, if a player was cursed they could use the altar to
remove the debuff.

> It was the unmistakable mark of a church, of which at least one exists in
> every town. And through the altar inside, tasks such as removing the attack
> unique to monsters, «Curse», and the blessing of weapons to go up against
> undead monsters with, were possible. In SAO, where magic-based components
> barely exist, it could be considered a most mysterious place.

As for Elucidator, the light novel describes this as a demon sword, not a
magic sword. However, both the English sub and dub refer to it as a magic
sword. As discussed in the comments, I believe this is an error in
translation. So there are no magical weapons in SAO, but they do seem to have
other forms of magic.

[![Picture from the anime of the "magic
sword"](https://i.stack.imgur.com/DYngs.jpg)](https://i.stack.imgur.com/DYngs.jpg)

> One is «Player made», which meant weapons made by us blacksmiths. The other
> included weapons that one gained from adventuring as «Monster drops».
> Needless to say, blacksmiths don't like drop weapons all that much. I
> couldn't even begin to count all the names like 'Unnamed' or 'No brand' that
> were given to them. But this sword seemed to be a very rare item amongst
> monster drops. If you compared the average quality of player-made weapons
> and monster drops, the former was better. But once in a while, «Demon
> Swords» such as this one appeared— that was what I heard.


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