proof the triangle inequality is needed to show the existence of the spherical building at infinity. In fact each known proof of the existence of the spherical building at infinity uses, in one way or another, the retraction appearing in axiom (A5) or the triangle inequality for the distance function on the building $X$, which is proved using (A5).

Axiom (A5) being equivalent to (A6) plus triangle inequality in case $\Lambda={\mathbb{R}}$ suggest that we should find a purely combinatorial proof of the existence of the building at infinity in oder to obtain that axiom (A5) is superfluous in Definition \[Def\_LambdaBuilding\]. This is carried out in Section \[Sec\_infinity\].

Besides the alternative proof of the existence of a building at infinity we will, in this short note, mainly discuss alternative sets of axioms for generalized affine buildings. In the following subsection we define generalized affine buildings and list the properties in consideration. For details we refer the reader to [@Diss] and [@Bennett].

Equivalence of axioms
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The model apartment of a generalized affine building is defined by means of a (not necessarily crystallographic) spherical root system ${\Phi}$ and a totally ordered abelian group $\Lambda$. As the apartments of Euclidean buildings are isomorphic 