• # Question: Maths Question! 1+1-1+1-1+1-1+1-1+1 ... to infinity can equal both 1 and can also equal an infinitely negative even number. Lets call ( 1+1-1+1-1+1-1+1 ... to infity ) A. If I multiply A by A, then I end up with 1-1+1-1+1-1+1-1+1-1... to infinity Which can equal either 0 or it can equal and infinitely negative odd number, so does that mean, 1 x 1 = 0? Or even that an inifinitely negative even number multiplied by and infinitely negative even number = an infinitely negative odd number? Have I just broken maths? :D. I have my maths teacher stuck on this one.

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Asked by bleddy to Angela, Gabriele, Karen, Maria, Shane on 15 Nov 2013.
• Gabriele De Chiara answered on 15 Nov 2013:

Eh eh! No tricks! You are showing a very clever example of a non convergent infinite series. The explanation is that A does not exist because the series is not uniformly convergent. So you cannot make multiplications of A with itself, it simply does not make sense. However it is very tricky. I’ll show you another one: say that a=b,
therefore a^2=ab
therefore a^2-b^2=ab-b^2
but (a^2-b^2 =(a-b)(a+b) dividing by a-b we get
a+b=b
but since a=b we get
2b=b and simplifying
2=1!!!!!!!
Where is the error?

• Karen McCarthy answered on 15 Nov 2013:

I’m no good at maths unfortunately, but obviously you are Bleddy! Nice question (I love stumping my teacher too!:) )

• Angela Stevenson answered on 18 Nov 2013:

Great job guys! I agree with Karen, if you ve got your maths teacher puzzled, then you must be a math whiz bleddy – great!