When I was a 4 year old, I traded my "neato" Champion cast iron motorcycle cop atop a motorcycle for a paper airplane.  I did it because I was fascinated with the new flying object.  I wasn't dumb but I was ignorant of value.  I didn't realize what I had given up until it was too late.  I still regret my ignorance.  Far into my adult life I was gifted with an almost exact antique cast iron cop atop his cycle by a dear friend.  Not all bad trades get undone even in the course of a lifetime. 

Too Late.

What a vast territory was the Louisiana Purchase.  The general population of the United States at that time had no idea how large a piece of land this was.  Nor what it cost ($15,000,000).  To say it was a bargain even at the time is a ludicrous statement that has no real meaning - like Manhattan Island for $24 in trinkets.  But remember the Louisiana Purchase did not include the lands Northwest of the Continental Divide and the Southwest lands including Texas etal  (those were stolen later.)  The French, Spanish, and British bandied the territory about for decades but it was originally stolen fair and square. 

The French and Spanish and British owned it by turns without clearing any deed through the resident Native American residents because the Native People were ignorant of European land laws etc. and land ownership was actually a novel concept for them. Then we perpetuated the crafty European myth that the Natives had no title to the land because, first of all, no King, Emperor, or Grand Poo-Bah anointed by God had issued a grant or deed.  Besides, indigenous "Indians" were considered imperfect heathens with no Human Rights.

However, our contract with the French gave us the "right" to gain the ultimate ownership of the lands by purchase or conquest (theft by another name.)  Plus, you know, they weren't farming it or building big cities so they forfeited the land by their neglect.  And we thereby justified our "theft."  Still,  it's ours and we got it the same way most the lands of the earth have been "owned" by someone - by conquest.  That includes native tribes excepting the very first native settlers who lived on hitherto unoccupied lands and laid claim to them.  Never mind all that, we were bigger and stronger and we took it. 

Only Jefferson realized what his purchase entailed so it had to be explored.  Lewis and Clark found out the hard way that the Rockies drained in both directions and at the end of the far West was the Great Pacific Ocean.  What L & C accomplished  with their expedition was pretty extraordinary. But the really detailed exploring for this nation of the United States of America was done by the type of men in the painting above.  Men combing every inch of land looking for furs. 

It's in the books.  You can look it up.