Nominal vs Real rate bond

Super simple question:

Why are real rate bonds the ones that change with inflation?

Nominal rate = (1+real rate) * (1+inflation), so doesnt this mean the nominal rate is adjusted for inflation and therefore the nominal rate bond includes inflation?

Where did you get the conclusion from?

I made the conclusion, tiantianangina. The nominal rate is the real rate adjusted for inflation… why is the nominal bond not the one thats adjusted for inflation?

“adjusting for inflation” is subtracting inflation from nominal instead of adding inflation to real