Third versus The third

[Van Khanh]

Please tell me the difference in meaning btw “the third” and “a third” in:

a. The third of 2.
b. A third of 2.
c. The third of a liter.
d. A third of a liter.

Thanks
K

[Yankee]

.
a. The third of 2. --> Makes no sense whatsoever

b. A third of 2. --> Means 2 has been divided into 3 parts and you are referring to one of the parts.

d. A third of a liter. --> similar to b.

c. The third of a liter. --> Makes sense only if which third of a liter has been previously mentioned/identified.
.

[Van Khanh]

Hi Yankee,

Do you think

"The third power of 2" and "the third of two" have the same meaning?

(I ask so because "Two to the third power " has the same meaning as "Two to the third").

Thanks
K

[Yankee]

.
It's possible that two crazy mathematicians might understand "the third of two" to mean "the third power of two" if they were in the middle of a fascinating conversation about "to the power of". But I wouldn't consider it to be a typical or "standard" short form. It would be too easily misunderstood.
.
"The third of 4" would typically be understood to mean "the third thing in a series of 4 things".
.

[Van Khanh]

Hi Yankee,

Your explanation took me out of my sleep. It's very interesting.

Khanh