0.999999.... equals 1

 Some will argue it doesn't

lets take the number N to be 10
multiply it by 10
so 10N = 100
now take away the original N
10N -N = 100 - 10
9N = 90  N = 90/9  N = 10

Lets try this again

eq (a) so lets take N = 0.99999999....

multiply it by 10
eq (b) 10N = 9.9999999....

take away the original Neq (b) - eq (a)  10N-N = 9.9999999.... - 0.99999999....eq (c)   9N  = 9            N = 1
take equation (c) N=1 and substitute into equation (a) N=0.99999999....and you get
1 = 0.99999999....

Where is the flaw in maths

Ref:
1.  How not to be Wrong.  The power of Mathematical Thinking.  Jordan Ellenberg