If you are old enough to be feeble, how do you feel about strangers offering to assist you?

Yesterday, I was in my college cafeteria, and I saw an elderly gentleman carrying his dishes to the dish return. He was limping, and his hand was shaking badly enough to make his dishes rattle loudly. I immediately wanted to help, but I was afraid he would perceive it as an insult.

I have known several elderly people who adamantly insisted on doing everything for themselves because they felt useless when people did things for them. Often, they would look for ways to help me so they would feel like they were contributing something in life. This is not just my perception of what they thought/felt; they actually said this.

So, if you are elderly and somewhat feeble, how do you feel when strangers offer to assist you? Do you feel differently if it is someone you know that offers to help? If you are getting close to that point in life, how do you think you will respond?