Is Tokyo a city?

Obviously, considering I am writing the questions and the answers to this section, the answer is more than a simple yes. 

The city of Tokyo ceased to exist on July 1, 1943 when the Tokyo prefectural government and the Tokyo City government agreed to merge.  The office of Mayor was eliminated and the governor took over the responsibilities of his responsibilities.

Today many people, for the sake of translation, still refer to Tokyo as a city.  It is easier to think of it that way.  This becomes especially confusing when the Japanese word for "prefecture" is investigated.  Japan has 47 prefectures and most of them are referred to as ken, meaning "prefecture".  Chiba Prefecture is known as "Chiba-ken" in Japanese.  "Aomori-ken", "Nagasaki-ken", et cetera.  For the most part this is how it goes, but there are a few exceptions.  Hokkaido is actually "Hokkai-do" with the do, for lack of a perfect equivalent in English, meaning "prefecture".  Meanwhile Osaka Prefecture and Kyoto Prefecture are known as "Osaka-fu" and "Kyoto-fu", with the fu delineating a majority urban prefecture.

Lastly is Tokyo Prefecture, known as "Tokyo-to", which is pretty much a substitute for "Prefecture", but can also be translated as "Metropolis" and entails both the area that was the countryside of the old prefecture, and what was once the city.  Today the countryside is mostly urbanized with the exception of the very western end.  The area that was once the city proper is today known as the Ward (ku) section of Tokyo-to.  There are 23 wards in Tokyo and today this area is known as "Tokyo-23-ku" (with "23" in Japanese of course).  Each ward is treated like its own city and has its own ward office, which is a defunct city hall.  Some translations will refer to each ward as a city ("The City of Shinjuku", "Kita City") but these borders are purely political. 

There are about a dozen other cities in Japan that have implemented the ward system.  Most recent of which was the city of Saitama, capital of Saitama Prefecture just north of Tokyo.  Before May of 2001, there was no such city as Saitama, only a prefecture of that name.  In the center of that prefecture were three major cities, Omiya, Yono, and Urawa, which had grown so big that the end of one city and the beginning of the other was only marked by a change in street signs.  It was one continuous urban sprawl.  With the merging, the three city governments became one and a ward system was implemented a year later.  The last time this happened was in 1963 with the creation of Kita-Kyushu, which had been a collection of about a dozen cities and towns.  (Including Kokura, which was the original candidate for the atomic bomb that was dropped on Nagasaki due to overcast skies.) 

What Exactly is the Population of Tokyo?

This has proven to be a tricky question for no other reason than for status.  According to some definitions, Tokyo is the largest city in the world.  Forget that Tokyo is not even a city for a moment and an investigation will show that as a city (meaning the 23 wards combined, what used to be the actual city), Tokyo ranks somewhere around seventh or eighth worldwide in terms of population, depending on the source and year of statistic. 

Certain sources vary the population of Tokyo the city by as much as a quarter of a million people.  According to the 2003 World Almanac, the ward section of Tokyo had a 1998 population of 7,854,000.  According to Japanorama (http://www.japanorama.com/cityrank.html), this same area has a population of 8,163,573, with no reference of the year this population existed.  And according to the World Gazetteer (http://www.world-gazetteer.com/home.htm), Tokyo has a 2003 population of 8,240,100, making it the 15th largest city in the world.  Which is the lowest I have ever seen it in world rankings.  (Mumbai (Bombay) and Buenos Aires rank at the top with over 12million each.  Which is the first time I have seen either so high on these lists.)

But, as with the Internet, each page about population statistics has a different figure and ranking.  So for the sake of sanity, I will trust what the United Nations has to say about population.