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Why is addition countable?

can someone explain to me why addition is countable when it is a finite sequence of terms separated by + signs:
i.e.(x1 + x2 + ….+xk) or (13, 2 + 3 + 3, 10 + 11 + 12)
because i know to be countable it needs to have a one-to-one correspondence with Natural numbers. But if you have 13, 3 + 10 in you set doesn’t that not longer make it one-to-one and thus not countable

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