The 0.999...= 1 Controversy & Is Mathematics Fundamentally Flawed?

It's the biggest controversy in mathematics... the 0.999...=1 debate just won't go away. We examine and analyse all the common arguments and proofs for 0.999...=1. The controversial aspects are highlighted and the foundations of mathematics itself are questioned. Feel free to discuss the points raised in this video on your chosen forums and social media platforms.

Nobody can explain how the infinitely many points 0.9, 0.99, 0.999, ... can exist all at the same time, at different positions on the number line, without there being a last one. But mathematicians seem content to accept that they just can. They claim we can simply restrict ourselves to talking about ‘the limit’, and that by ignoring the problem of the last point we can claim that “there is no problem”.

This uncovers one (of the many) fundamental problems of mathematics, which is that there is no rigour about what forms an inconsistency/absurdity/contraction.

For example, say one group of people believe that it forms a trivial contradiction to claim that a decimal with endless non-zero trailing digits (such as the decimal for the square root of two, 1.41421...) can be said to equal a constant value. However, another group of people might disagree, and so which side is right?

Since maths is supposedly 'abstract' we can’t examine this scenario in the real world in order to determine which side is correct. All we have are make-believe arguments about a make-believe scenario. And so even though the second group have devised a large amount of subjective make-believe clever-sounding arguments to support their position, the first group will remain defiant.

Perhaps this is the main reason why the 0.999...=1 debate just won't go away?