Republican presidential nominee Donald Trump offered an aggressive 10-point plan Wednesday to crack down on illegal immigration, including the creation of a "deportation task force" and a pledge to deport people living here illegally who are arrested for crimes.

Trump reiterated his pledge to build a wall along the southern border -- with aerial and ground sensors -- and promised that Mexico would pay for construction. He said he’d create safe zone for refugees leaving Syria, and that the Gulf states would pay for them. And he vowed to reverse immigration policies in nearly two dozen countries that leave people scheduled to be deported stuck in America.

"Mexico will work with us. I absolutely believe it. And especially after meeting with their wonderful, wonderful president today, I really believe they want to solve this problem along with us, and I'm sure they will," Trump said in Phoenix.

PolitiFact is fact-checking several claims from Trump’s speech, some of which cover familiar territory.

"Hillary Clinton has pledged amnesty in her first 100 days, and her plan will provide Obamacare, Social Security, and Medicare for illegal immigrants, breaking the federal budget."

There's no 100-day pledge for amnesty. Clinton has promised to submit a plan to deal with the immigration issue in her first 100 days.

Clinton does support policies that would let some illegal immigrants stay in the country for now and allow them to work. As a result, under longstanding federal policy, if they're working they're paying into Social Security and Medicare. They might someday be eligible to collect benefits if they've worked long enough and are old enough.

Clinton also supports letting illegal immigrants buy Obamacare policies, but not with federal assistance. They are not eligible for Medicaid.

And because, under the circumstances, this would not break the federal budget, Trump gets a Mostly False.

"The truth is, the central issue is not the needs of the 11 million illegal immigrants or however many there may be -- and honestly we've been hearing that number for years. It's always 11 million. Our government has no idea. It could be 3 million. It could be 30 million. They have no idea what the number is."

No credible estimate suggests the undocumented population is as low as 3 million or high as 30 million. That statement rates Pants on Fire.

The government and analysts across the partisan aisle have more of an idea about the size of the undocumented population than Trump says. The Department of Homeland Security says the number of illegal immigrants was about 11.4 million as of January 2012. Other independent groups that research illegal immigration put the number between 11 and 12 million.

Jeffrey Passel, a demographer at the Pew Research Center, called both of Trump’s numbers "virtually impossible" and explained why. On the low end, survey data shows large enough foreign-born populations and legal admissions that there could not be as few as 3 million people.

The high-end of Trump’s offered estimate is contradicted by the limited number of housing units in the United States, Mexico and Central America’s census data and surveys’ size, and U.S. data on admissions and departures.

"There’s simply no way for an additional 20 million people to be in the country and have escaped detection," Passel said.

"Illegal immigration costs our country more than $113 billion a year."

Trump presented the $113 billion figure as a fact, but that number is a rough, high-end estimate. We rated that statement Mostly False.

Trump’s number stems from a 2013 report from Federation of American Immigration Reform, a group favoring reduced immigration. The $113 billion estimate does not take into account tax contributions from undocumented immigrants. Factoring in those payments, the group's estimated net cost of illegal immigration is around $99 billion.

Still, many immigration experts remain skeptical of such a high estimate. The report highlights the fiscal costs of undocumented immigrants at federal, state an local levels, but its estimates include at least 3.4 million U.S. citizens — children born in the United States to parents living in the country illegally.

We did not find an exact dollar amount for the cost of illegal immigration, but other groups have estimated much lower costs.

"President Obama and Hillary Clinton have engaged in gross dereliction of duty by surrendering the safety of the American people to open borders, and you know it better than anybody right here in Arizona. You know it."

This is another inaccurate claim repeated by Trump and his surrogates. Under President Barack Obama, deportations of undocumented immigrants have reached record highs, even as that population has fallen in recent years. And it was not the role of Clinton’s State Department to enforce the nation’s immigration policies.

The current administration’s focus has been to quickly return people crossing the border illegally.

As a presidential candidate, Clinton has proposed addressing immigration laws including a path to citizenship within her first 100 days. But she has also called for protecting borders and deporting criminals or those who pose threats.

Clinton’s immigration platform does not amount to open borders, Alex Nowrasteh, an immigration expert at the libertarian Cato Institute, previously told PolitiFact Florida when we fact-checked a similar claim by Trump that we rated False.

Open borders existed before 1875, when there were no federal restrictions on emigrating to the country, he said. The United States had immigration restrictions from 1875 to 1924 without a border patrol, which was created in 1924.

It’s wrong to conflate "open borders" with anything less than perfect enforcement of immigration laws, he said. It’s also wrong to "claim Clinton is for open borders while she has also supported massive increases in border security to better enforce our restrictive immigration laws."

"There are at least 23 countries that refuse to take their people back after they’ve been ordered to leave the United States, including large numbers of violent criminals."

We rated this statement Mostly True.

The 23-country figure is backed up by a U.S. Immigration and Customs Enforcement document. Remarks from Daniel Ragsdale, the deputy director of ICE, mention that ICE identified 23 "recalcitrant" countries, including Afghanistan, Algeria, China, Cuba, Iraq, Libya, Somalia and Zimbabwe.

The other part of Trump's claim is harder to prove. Out of all convictions for anyone known to be in the United States illegally in 2015, 101 were for homicide, while more than 30,000 were for traffic-related or drug-related offenses. We could not find a breakdown for criminal immigrants who were ordered to leave the United States but were not returned to their home countries.

"Since 2013 alone, the Obama administration has allowed 300,000 criminal aliens to return back into United States communities. These are individuals encountered or identified by ICE, but who were not detained or processed for deportation because it wouldn't have been politically correct."

Trump’s description of the number in his speech is not entirely accurate. On balance, we rate it Half True.

One can make a reasonably strong -- though not foolproof -- case for 100,000. But immigration professionals are divided over how credible the next 200,000 is.

"You know this, this is what they talk about, facing American society today is that there are 11 million illegal immigrants who don't have legal status. And, they also think the biggest thing, and you know this, it's not nuclear, and it's not ISIS, it's not Russia, it's not China, it's global warming."

PolitiFact has examined similar claims about Obama before, rating them Mostly False.

Obama has said climate change is a great threat to the world, but he has said repeatedly fighting terrorism is his most urgent priority.

In March, after the terrorist attacks in Brussels, Obama said, "I’ve got a lot of things on my plate, but my top priority is to defeat ISIL."

"Approximately half of new illegal immigrants came on temporary visas and then never, ever left. Why should they? Nobody's telling them to leave. Stay as long as you want, we'll take care of you."

That’s largely accurate and a claim we’ve rated Mostly True in the past. The numbers are estimates here based on limited data, but they're credible.

In a 2006 report, Pew Research Center estimated that "nearly half of all the unauthorized migrants now living in the United States entered the country legally through a port of entry such as an airport or a border crossing point where they were subject to inspection by immigration officials." While the source data gave an estimate that ranged from 33 percent to 50 percent, the report went middle-of-the-road and called it 45 percent.

That report relied on a 1997 study from the Immigration and Naturalization Service. While trying to ascertain how many immigrants arrived and departed, INS concluded that in 1996, 41 percent of illegal immigrants had entered the United States legally.

Because federal agencies haven’t provided new data, there’s little for analysts to use to provide an updated figure. Experts (including the demographer who created the initial estimate) told us that while illegal immigration trends have changed over the years, 40 percent can still be considered an acceptable estimate.