Your sentence is correct.
Yes, you can end a sentence with a preposition. Some people think you can't but you can.
As Winston Churchill once said, "That is the sort of English up with which I will not put."
Most of us would simply say, "That is the sort of English I will not put up with."
Without - Using GuruNet.com....
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with·out (wi(TH-out', wi(th-)
adv.
On the outside: a sturdy structure within and without.
With something absent or lacking: had to do without.
prep.
Not having; lacking: a family without a car.
Not accompanied by; in the absence of: volunteered without hesitation; spoke without thinking.
At, on, to, or toward the outside or exterior of: standing without the door.
n.
An outer position, place, or area: a threat to security that came from without.
conj. Regional.
Unless: “You don't know about me without you have read a book by the name of The Adventures of Tom Sawyer” (Mark Twain).
[Middle English withoute, from Old English withu-tan : with, with; see with + u-tan, from without (from u-t, out. See out).]
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The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2003 by Houghton Mifflin Company.
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Thus, we see that without is not ALWAYS a preposition, but when it means "Not having; lacking," it is. So in our case, it is a preposition.
As we said at the outset, it is okay to end a sentence with a preposition.
"The mission of our foundation is to provide services and financial assistance to facilitate fully the integration of children with disabilities into the life environment of those without."
As a complete aside, if it were me, I would rewrite your mission statement.
"The mission of our foundation is to provide services and financial assistance to children with disabilities so that they can lead as happy and enjoyable lives as possible with their friends, family, and the rest of society."
Maybe something like that?
When I am dealing with people, I dislike using "facilitate, maximize, minimize, impact, -tion words" and the like. It reminds me of too much committee work where people have lost sight of the real purpose. But that's just me. Everyone is different. I thought I would share my opinion for some additional food for thought. It's only worth what you paid for it.
I hope this message is of benefit.
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