How to Explain the Elementary Theory of an Ideal Transformer?

Ideal Transformer does not exist according to the Elementary Theory

A transformer can never be an ideal device to transfer power. Theoretically, an ideal transformer is useful in understanding the practical transformer. Because a Transformer, inherently design has limitations caused by losses within the device itself, like- transformer Core Loss and Transformer Copper Loss. An ideal transformer considers there are no losses, it transfers the same power that it received.

The Characteristics of an ideal Transformer

A transformer to be an ideal transformer, it needs such a transformer which has no losses i.e. transformer windings have no ohmic resistance, there will happen no magnetic leakage and hence which has no I²R and core losses. 

So the ideal transformer should have two purely inductive coils wound on a loss-free core.