**Statement One:** $\text{Let} \ 0.4\overline{9} = x$

**Statement Two:** $\implies 10x = 4.\overline{9}$

**Statement Three:** $100x = 49.\overline{9}$

**Statement Four:** $\implies x = 0.4\overline{9} = \cfrac{45}{90} = \cfrac{1}{2}$

Since from **Statement Four:** , $0.4\overline{9} = \cfrac{45}{90} = \cfrac{1}{2}$ , multiplying both sides by 2,

**Statement Five:** $\implies \left[ 0.4\overline{9} \right ] \cdot 2 = \left[ \cfrac{1}{2} \right ] \cdot 2 = 1$

Upon multiplying, we see that

**Statement Six:** $\left[ 0.4\overline{9} \right ] \cdot 2 = 0.\overline{9}8 = 1$

**Statement Seven:** But upon searching, famously, $1 = 0.\overline{9}$

**Statement Eight:** $\therefore 0.\overline{9}8 = 0.\overline{9}$

But, it will break the **"reflexive property of equality"** .

Which Statement Is The Start Of The Mistake In The Said Argument?

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