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The phrase "am wrong" is correct and usable in written English, though it is typically part of a larger sentence.
You can use it when admitting a mistake or acknowledging an error in judgment.
Example: "I realize now that I am wrong about the project's timeline."
Alternatives: "I was mistaken" or "I made an error."
Dictionary
am wrong
adjective
Incorrect or untrue.
Exact(60)
I am wrong.
Hopefully, I am wrong".
I hope I am wrong.
But I am wrong again.
But apparently I am wrong.
I dearly hope I am wrong".
"I hope that I am wrong.
"I hope I am wrong," he added.
And yet, he says I am wrong.
"And if I am wrong, then so be it.
I don't see immediately that I am wrong.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com