"endless number" is a perfectly valid phrase in written English.
For example, "I have an endless number of tasks to finish today."
The document presents a seemingly endless number of questions.
They have bought dozens of plants, hammers and hoes and a seemingly endless number of wheelbarrows.
There are niches within subgenres and an endless number of series and sequels and prequels.
Throughout, there is swing, sure and steady, and a seemingly endless number of songlike phrases.
There are an endless number of traps that a new business can fall into.
I could have picked an endless number of Neil Young songs.
The endless number of people who have crossed your path will bear witness to this.
He eventually settled at station WHO, in Des Moines and recalled attending "an endless number" of auto races.
One stack had the names and definitions of the seemingly endless number of organic compounds I had to memorize.
There seem, potentially, to be an endless number: the war's capacity to create new militants is limitless.
Yet sports collecting is fueled by an unending flow of players who wear an endless number of uniforms and gear.
