Spivak's "Calculus on Manifolds" defines the wedge product between a $k$-form and a $l$-form (alternated tensors $\in \Omega^k(V), \in \Omega^l(V)$ respectively as:

$$\omega(v_1,\cdots,v_k)\wedge \eta(v_{k+1},\cdots, v_{k+l})=\frac{(k+l)!}{k!l!} \frac1{k!} \sum\text{signed permutations} $$

I'm writing "signed permutations" to mean, for example with two one-forms:

$$ \omega(v_1)\wedge \eta(v_2) = \frac{(1+1)!}{1!1!}\frac1{1!}\omega(v_1) \eta(v_2) - \omega(v_2) \eta(v_1) $$

Anyway. Arnold's "Mathematical Methods of Classical Mechanics" defines the wedge product without the constant -- just the sum of signed permutations; so his product of two one-forms is half of Spivak's.

Is this a physics/pure maths difference in convention (so the constant factor doesn't matter in physics), or is this factor usually accounted for elsewhere in different expositions of the theory (for example, in exterior differentiation or symplectic forms, etc.)?