Equivalent Exchange
The rule the Elrics begin with — not a promise that life will be fair
Edward and Alphonse grow up treating Equivalent Exchange as alchemy's basic rule: if you want to obtain something, something of appropriate value has to be given.
For ordinary transmutation that means understanding the material you are changing and working with what is actually there. Brotherhood does not need the viewer to imagine every alchemist performing an invisible atomic calculation.
The important part is what Ed does with the rule. He turns a principle of alchemy into a philosophy of life, then spends the series discovering that effort, suffering and reward do not arrive in perfectly balanced amounts.
Why it matters
Equivalent Exchange is where Ed starts. His final answer is not that the rule was useless. It is that people cannot reduce every human relationship to a transaction.
Human Transmutation & the Gate
Forbidden resurrection · knowledge gained at a physical toll
Edward, Alphonse and Izumi all attempt the same impossible thing for the same human reason: they want somebody dead to come back.
The result is not resurrection. The transmutation opens the Gate, exposes the alchemist to Truth and takes a toll. Edward loses his left leg, Alphonse loses his entire body, and Izumi loses internal organs. Edward then sacrifices his right arm to bind Al's soul to armor.
What changed
The taboo is not important because the military wrote a rule against it. It is important because the brothers' entire journey begins after they learn that knowing how to perform alchemy does not mean alchemy can give them whatever they are desperate enough to ask for.
Amestrian Alchemy vs. Xingese Alkahestry
Two traditions that do not feel the same world beneath their feet
Amestrian alchemists explain their power through energy associated with movement in the earth. Xingese alkahestry reads a different flow, the Dragon's Pulse, and develops especially strong medical and long-range applications from that tradition.
The difference becomes a plot clue when May realizes that something about the energy beneath Amestris feels wrong. Later, Father demonstrates that he can interfere with ordinary Amestrian alchemy while Xingese alkahestry continues to function.
Why it matters
May is not arriving with a cosmetically different magic system. She is the outsider who can feel that Amestris has been living on top of an artificial layer its own alchemists never knew was there.
Myth: Alphonse's Soul Is Made of or Stored Inside the Armor
The armor is an anchor, not the soul itself
Alphonse is not a suit of armor that somehow became alive. Edward bound Al's soul to the armor with a blood seal after Al's body was taken at the Gate.
That seal is the connection keeping the soul attached to the armor. Damage to the metal can be repaired because the metal is not Al's body, but destruction of the blood seal would sever the anchor keeping him in the armor.
Why it matters
This is why Al can survive damage that would kill a human and still be terrifyingly vulnerable to one small mark inside the suit. His apparent invulnerability depends on something physically fragile.