Question Number 3994 by Filup last updated on 26/Dec/15
$$\mathcal{A}\mathrm{re}\:\mathrm{there}\:\mathrm{more}\:\:\mathcal{T}{rancendental} \\ $$$${or}\:\mathcal{N}{on}-\mathcal{T}{rancendental}\:{numbers}? \\ $$$$ \\ $$$$\mathcal{NOTE}: \\ $$$$\mathcal{T}{rancendentals}\:{are}\:{numbers}\:{that} \\ $$$${cannot}\:{be}\:{written}\:{algerbraically}. \\ $$$$ \\ $$$${e}.{g}.\:{x}^{\mathrm{2}} =\mathrm{2} \\ $$$$\therefore\sqrt{\mathrm{2}\:}\:\mathrm{is}\:\mathrm{non}-\mathrm{trancendental} \\ $$$$ \\ $$$$\pi\:\mathrm{is}\:\mathrm{transendental} \\ $$
Commented by prakash jain last updated on 26/Dec/15
$$\mathrm{Set}\:\mathrm{of}\:\mathrm{algebraic}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{countable}. \\ $$$$\mathrm{Set}\:\mathrm{of}\:\mathrm{trancsdental}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{not}\:\mathrm{countable}. \\ $$
Commented by Filup last updated on 26/Dec/15
$$\mathrm{How}\:\mathrm{can}\:\mathrm{we}\:\mathrm{prove}\:\mathrm{it}? \\ $$