Funny paradox

There are two cups of water, which are both half-full. Then: $\text{half full }=\text{ half space}$ Multiply 2 both sides: $\text{full }=\text{ space}$ Which means everything can turn into nothing! Can you find the mistake?

#Logic

Easy Math Editor

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Comments

The half full=half space , is an abstraction of the quantity of the water(Volume) in the cup, hence at the end of the argument, essentially what you are saying is that the volume of a cup filled with water= to the value of the empty cup!, which is indeed true!. The only flaw is that you take into account the mathematical statement of full=space, which is a result of abstraction created by the 1st statement "There are two cups of water, which are both half-full" . The ' half full = half space " only makes sense if you are talking of the quantity, a meaning which is implied (not explicitly stated) AND THEN when you perform normal arithmetic you only take into account the mathematical statement not with respect to the initial context.

Sarthak Sahoo - 1 year, 5 months ago

Ya that's right

Isaac YIU Math Studio - 1 year, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$