This is the limit!

Algebra Level 1

Is the equation below true?

$4.99999999999999999999999999999999\ldots = 5$

Yes No

4 solutions

Andrea Virgillito
Mar 27, 2016

It isn't actually an equation

Paco Escobar
Feb 26, 2016

Knowing that $\frac{1}{3}$ = $0.\overline {333}...$ and $0.\overline {999}...$ $=3*\overline {0.333}...$ then $3*$ $\frac{1}{3}$ $= 1$ so $0.\overline {999}...$ $= 1$ .

Now, for this problem, we need to subtract 4 from both sides and we will end up with $0.\overline {999}...$ $=1$ , which was demonstrated to be true on the first part of this solution.

Moderator note:

Great! It's often better to work in one direction. In this case, we can simply continue from the first line and say "add 4 to both sides".

It is actually wrong.

Aakhyat Singh - 3 years, 9 months ago

No matter up to how many 9's the number goes, it will be never equal to 5

Aakhyat Singh - 3 years, 9 months ago

because you can always add a number 0.000000......00001 to 4.99999......, and you can't argue that 0.00000....000001=0

Aakhyat Singh - 3 years, 9 months ago

Kay Xspre
Feb 24, 2016

On the other hand, if we subtract 4 for both sides it's like the proof that $0.\overline{9} = 1$ . Several questions are previously arguing whether it was or was not the same, and the proof shows it was indeed equal , while others are not much convincing.

Onkar Shirodkar
Feb 24, 2016

The answer is Yes.
370/90=4.1111⋯
380/90=4.2222⋯
390/90=4.3333⋯
400/90=4.4444⋯
410/90=4.5555⋯
420/90=4.6666⋯
430/90=4.7777⋯
440/90=4.8888⋯
Hence,
5=450/90=4.9999⋯

This is the limit!

4 solutions

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