Despite the alleged proof of Cantor's theorem, Wittgenstein commented on the use of this statement in agreement with transfinite numbers. In his Observations on the Foundations of Mathematics, Wittgenstein noted that while Cantor may say 2^(ℵ_0 )>ℵ_0 it is “a piece of mathematical architecture which is suspended in the air, and looks as if it were, say, a lintel, but unsupported from nothing and supporting nothing." While we can consider Cantor's theorem, it doesn't actually inform us about the context of 2^(ℵ_0 ). So we have no more information about this apparent cardinality of the real numbers. Without any concept of what sense or concept we are actually giving to this cardinality, we can say very little about the number of elements in the set of real numbers. Therefore to suggest conclusively that there are more real numbers than natural numbers, without taking into account what this means, seems ambiguous and consequently