SPP claims 9+0.(9)=9.(9)

9.(9) is simply 0.(9)*9 also as said by SPP. Thus, 9.(9)=0.(9)*9. Additionally, 9.(9)-0.(9)=10*0.(9)-0.(9)=9*0.(9) by distributive property. 9.(9)-0.(9) is also equal to 9+0.(9)-0.(9)which is equal to 9. So, 9=9*0.(9). By the fundamentals of algebra, 1=0.(9).