(Please all of you be patient and give me your feedbacks whether the following ideas false or true ,whether they are useful or useless, also tell me in your opinions how can I improve these ideas if they are good.)Consider the following set :
$\{0.1,0.01,0.001,...\}=\{10^{-n}:n \in \mathbb{N}\}$
then $\lim_{n \to \infty} 10^{-n}=m $ (I consider m in the context of my ideas that it is the smallest positive real number)
Let
$M=\{...L_{-1}=-1-m$ ,L_{0}=-m (the largest negative number) , L_{1}=1-m=0.999999.... ,... }
={L_{r}=r-m : $r \in \mathbb{Z}$ }$ **(I know 0.999...=1 it has proof but it is still not convincing in my opinion)
Can I consider elements of set $M$ irrationals of type transcendental?
Following I want to show you this idea using m (the smallest positive real number from above):
Let $s=((90-m)degrees$
$\tan{(s)}=\frac{\sin {(s)}}{\cos{(s)}}=\frac{1-m}{m}=\frac{1}{m}-1$(very big number) while $\sec{(s)}=\frac{1}{\cos{(s)}}=\frac{1}{m}$ (also very big number)
so can I say that $\tan{(s)}$ < $\sec{(s)}$?