As part of Facebook's Internet.org initiative, the project would provide Internet access to certain areas of Africa that currently can't get online.
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The social-networking giant has begun lobbying the United Nations, saying Internet access is a fundamental human right.
In a question-and-answer session at Facebook's headquarters, Indian prime minister discusses governing through social media and expanding Internet access.
The initiative's goal is to provide Internet access to the nearly 1 billion people in India who aren't online.
Website backed by the social networking giant to expand Internet access globally is renamed Free Basics.
Commentary: Pope Francis isn't a fan of unfettered capitalism, but that doesn't mean capitalists won't capitalize on his visit.
Before visiting the US, President Xi Jinping said China is a hacking victim, too, and suggests both countries will benefit from computer security cooperation.
Modi, one of the world's most tech-savvy politicians, will join Mark Zuckerberg to discuss a variety of subjects, including how communities can address social and economic challenges.
The countries are in talks to prohibit first strikes against critical infrastructure, according to The New York Times. The negotiations could lead to first-ever arms-control deal for cyberspace.