At the start of the novel, the narrator introduces Carrie’s naive worldview by employing verbal irony and foreshadowing. They hint at the vast changes and travels awaiting her:
To be sure there was always the next station, where one might descend and return. There was the great city, bound more closely by these very trains which came up daily. Columbia City was not so very far away, even once she was in Chicago. What, pray, is a few hours—a few hundred miles?
Dreiser uses the phrase "to be sure" in the novel many times. Every instance of this phrase is a moment of verbal irony. While ostensibly denoting confidence or certainty, “to be sure” in Sister Carrie is almost always utilized in contexts where a character is on the cusp of a misunderstanding or miscalculation. It's dangerous, Dreiser implies, "to be sure" of anything.
Here, the irony lies in Carrie’s sense of surety in the face of her limited experiences: "What, pray, is a few hours—a few hundred miles?" For someone like Carrie—who has never ventured outside of Wisconsin—such distances would have been monumental. Before high-speed travel like airplanes and cars became widely available, moves like her relocation from Wisconsin to Chicago would have been major lifetime events.
The passage also foreshadows the trajectory of Carrie's life. Throughout the course of the novel, the protagonist will make some major geographical moves, and this quote hints at the various cities and experiences in her future. The allusion to "the next station" and the possibility of descent and return suggests the choices and changes coming to Carrie's life. The implication is that once Carrie is swept away by her new life, a return to her roots will become an increasingly remote possibility. The phrase, "Columbia City was not so very far away, even once she was in Chicago," subtly emphasizes this impending chasm between her past and future.
Carrie's personal aspirations to better herself lead her to spend part of her scanty funds on an umbrella. This situationally ironic choice, influenced by vanity, results in a rift with her financially conscious sister, Minnie. It also foreshadows Carrie’s later troubles:
On the first morning it rained [Carrie] found that she had no umbrella. Minnie loaned her one of hers, which was worn and faded. There was the kind of vanity in Carrie that troubled at this. She went to one of the great department stores and bought herself one, using a dollar and a quarter of her small store to pay for it.
"What did you do that for, Carrie?" asked Minnie, when she saw it.
"Oh, I need one," said Carrie.
"You foolish girl."
Carrie resented this, though she did not reply. She was not going to be a common shop-girl, she thought; they need not think it, either.
The irony here is multifaceted. Carrie wants to buy an umbrella because the one that’s being offered to her will make her look poor. However, she’s too poor to afford an umbrella without risking her financial future. Carrie's actions, driven by a need to appear as if she has disposable income, ironically bind her closer to a reality she is striving to avoid. Purchasing the umbrella isn't merely about protection from rain; it's symbolic of her desire to shield herself from the judgments of society. If she has a nice new umbrella, she believes people won’t think she is “common.”
Furthermore, the incident provides foreshadowing; readers see early signs of Carrie's inclination towards luxury, even when it’s impractical or actually risky. This rash choice hints at future ones like it, informed by a mix of vanity and ambition.