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## Main Question or Discussion Point

Ok this is from a tutorial I am redoing again.

V5 = {(x, 1) | x ∈ R}, (x1, 1) ⊕ (x2, 1) := (x1 + x2, 1), c.(x, 1) := (cx, 1).

I understand that there exists a zero vector in this vector space, that comes in the form of (0,1). What I do not understand is why that is considered a zero vector for that vector space?

It is hard for me to 'see past' that 1 in the y-coordinate. Please ease my irritations, thank you :)

V5 = {(x, 1) | x ∈ R}, (x1, 1) ⊕ (x2, 1) := (x1 + x2, 1), c.(x, 1) := (cx, 1).

I understand that there exists a zero vector in this vector space, that comes in the form of (0,1). What I do not understand is why that is considered a zero vector for that vector space?

It is hard for me to 'see past' that 1 in the y-coordinate. Please ease my irritations, thank you :)