**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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